The US post office will accept packages whose combined height and perimeter of the base are at most 140 inches.
Use Lagrange multipliers to find the dimensions of the largest volume box that will be accepted.
Answers
The dimensions of the largest volume box that will be accepted are 35 x 35 x 35 inches.
Let's assume that the dimensions of the box are x, y, and z, where x, y, and z are all non-negative. The volume of the box is given by V = xyz. The combined height and perimeter of the base are given by 2z + 2(x + y) = 140, or z + x + y = 70.
To find the maximum volume of the box subject to this constraint, we need to use Lagrange multipliers. We want to maximize V subject to the constraint g(x,y,z) = z + x + y - 70 = 0. So we define the Lagrangian L as:
L(x,y,z,λ) = xyz + λ(z + x + y - 70)Then we take partial derivatives of L with respect to x, y, z, and λ, and set them equal to zero:
∂L/∂x = yz + λ = 0∂L/∂y = xz + λ = 0∂L/∂z = xy + λ = 0∂L/∂λ = z + x + y - 70 = 0Solving these equations simultaneously, we get:
x = y = z = 35λ = -35So the dimensions of the largest volume box that will be accepted are 35 x 35 x 35 inches.
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Related Questions
1. abundant trans bonds make partially hydrogenated vegetable oil a very unhealthy food choice. vegetable oil can also be hydrogenated until it becomes fully saturated with hydrogen atoms. would the physical properties of the hydrogenated and partially hydrogenated oils differ? if so, how and why would the differences occur? do you think that full hydrogenation makes vegetable oil more or less healthy to eat, or does it have no effect?
Answers
Yes, the physical properties of hydrogenated and partially hydrogenated oils are different.
Here are the differences that occur between them:-
Fully Hydrogenated Oils-
1.) Hydrogenated Oil is an oil in which all C=C bonds have been reduced.
2.) Oil returns to "zero trans fat" levels.
3.) Fully hydrogenated oils are probably healthier than partially hydrogenated oils because they contain no trans fats.
Partially Hydrogenated Oils -
1.) Partially hydrogenated oils have some an oil in which the C bonds have not been altered.
2.) Partial hydrogenation produces trans fats.
3.) Partially hydrogenated oils or trans fats are not food safe.
Yes, fully hydrogenated vegetable oils are more or less healthy or ineffective. Harmful forms of saturated fatty acids. Fully hydrogenated oils are solid, similar to the saturated fats found in meat. Fully hydrogenated oils are probably better than partially hydrogenated oils because they contain no trans fats.
It is hard to say that it is good for your health.
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a disaccharide is formed when two monosaccharide units react via their oh functional groups. the linkage in a disaccharide is
Answers
When two monosaccharide units react via their hydroxyl (OH) functional groups, a disaccharide is formed. The linkage between the monosaccharide units in a disaccharide is known as a glycosidic linkage.
The glycosidic linkage is a covalent bond that joins the two monosaccharide units together. It is formed through a dehydration or condensation reaction, where the hydroxyl group from one monosaccharide combines with the hydrogen atom from the other monosaccharide, resulting in the formation of a water molecule. The remaining oxygen atom from each monosaccharide forms the glycosidic bond.
The specific type of glycosidic linkage depends on the orientation of the hydroxyl groups involved in the reaction. Common types of glycosidic linkages include alpha and beta linkages. In an alpha linkage, the hydroxyl group involved in the reaction is positioned below the plane of the ring, while in a beta linkage, the hydroxyl group is positioned above the plane of the ring.
The type and position of the glycosidic linkage in a disaccharide determine its properties and functionality. Different disaccharides, such as sucrose, lactose, and maltose, have distinct glycosidic linkages, resulting in their unique structures and functions.
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The Tacoma narrows bridge collapsed due to?
A. Refraction
B. Reflection
C. Diffraction
D. Resonance
Answers
What element has more electrons than sodium, but less electrons than aluminum?
Answers
Answer: Magnesium
Explanation:
Sodium, number of electrons= 11
Aluminum, number of electrons= 13
Magnesium, number of electrons= 12. which is greater than sodium but less than aluminum.
Magnesium
What is the ph value of neutral substance
Answers
Answer:
Acidity and alkalinity are measured using a pH scale, for which 7.0 is neutral. The lower a substance's pH (less than 7), the more acidic it is; the higher a substance's pH (greater than 7), the more alkaline it is. Average rain has a pH of about 5.6; it is slightly acidic because carbon dioxide (CO2) dissolves into it, forming weak carbonic acid. Acid rain usually has a pH between 4.2 and 4.4. The most common nitrogen-related compounds emitted into the air by human activities are nitrogen oxides. Ammonia is another nitrogen compound emitted into the atmosphere, primarily from agricultural activities and fossil fuels. Most of the nitrogen oxides released in the U.S. due to human activity are from the burning of fossil fuels associated with transportation and industry.
Explanation:
Nuclear submarines can stay underwater for months in part because they can produce oxygen for the crew to breathe via the electrolysis of water. The half reactions for this process are provided: 2 H2O (1) → O2 (g) + 4 H* (aq) + 4e 2 H* (aq) + 2e¯ → → H2 (g) Calculate the minimum current needed (in amperes) to produce enough oxygen to meet the daily needs of a crew of 10 people. The average person needs 0.840 kg of O2 gas per day. Current =
Answers
For the given electrolysis of water reaction, the half reactions are as follows:2 H2O(l) → O2(g) + 4H+(aq) + 4e-2H+(aq) + 2e- → H2(g)The balanced equation is 2H2O(l) → 2H2(g) + O2(g)For producing one mole of O2 gas, 4 moles of electrons are needed (from the first half-reaction).
For producing one mole of H2 gas, 2 moles of electrons are needed (from the second half-reaction)Number of moles of O2 gas required per day = (10 × 0.840 kg)/32 kg mol-1 = 0.263 mol Number of moles of H2 gas produced per day = 0.5 × 0.263 mol = 0.132 mol.
Number of moles of electrons required = 4 × 0.263 mol = 1.052 mol The electric current required for producing 1.052 mol of electrons in a day = 1.052 × (96500 C/mol) / (24 × 60 × 60 s) = 0.012 AThus, the minimum current needed to produce enough oxygen to meet the daily needs of a crew of 10 people is 0.012 A. Current = 0.012 A.
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the enthalpy change for the reaction is -67 kj. is the reaction endothermic or exothermic? is energy absorbed or released as the reaction occurs?
Answers
Given that the enthalpy change for the reaction is -67 kJ, the reaction is exothermic, and energy is released as the reaction occurs.
Enthalpy refers to the amount of energy that is stored in a compound's chemical bonds or the heat released or absorbed during a chemical reaction. It is a thermodynamic property that determines the quantity of energy released or absorbed during a process such as chemical reaction or change in state.
When a reaction absorbs energy from its surroundings, it is known as an endothermic reaction. The reaction's enthalpy, which is the energy released or absorbed during a reaction, is positive. The system absorbs energy, which is why it is denoted by a positive value.
When a reaction releases energy into the surrounding, it is referred to as an exothermic reaction. The reaction's enthalpy, which is the energy released or absorbed during a reaction, is negative. The system releases energy, which is why it is denoted by a negative value.
Therefore, the reaction is exothermic and energy is released when the reaction occurs.
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anybody know the answer
Answers
Answer:
i think c
Explanation:
Alright, now you actually have an aqueous solution of your salt! Though perhaps not all of the salt has dissolved yet, but we'll get to that. How sure would you say you are about the concentration at this point?
a) What I've prepared is not yet an aqueous solution
b) It's not that accurate, but similar to what we need in the end
c) It's quite accurate
d) It's really inaccurate
Answers
If not all of the salt has dissolved then the measurement of the concentration at the time is really inaccurate.
What is concentration?The concentration is the amount of substance that is present in solution. We know that we can not measure the concentration unless all of the solute have been dissolved in the solution.
Thus, if not all of the salt has dissolved then the measurement of the concentration at the time is really inaccurate.
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When mixed, aqueous solutions of aluminum nitrate, Al(NO3)3, and ammonium carbonate, (NH4)2CO3, will form a precipitate of aluminum carbonate, Al2(CO3)3. The balanced equation is:
2Al(NO3)3(aq) + 3(NH4)2CO3(aq) à Al2(CO3)3(s) + 6NH4NO3(aq)
Which of the following statements regarding this reaction is incorrect?
A)2 moles of Al(NO3)3 will react with 3 moles of (NH4)2CO3.
B)If 6 moles of (NH4)2CO3 react with sufficient Al(NO3)3, 2 moles of Al2(CO3)3 will be formed.
C)If 0.5 mole of (NH4)2CO3 react with sufficient Al(NO3)3, 3 moles of Al2(CO3)3 will be formed.
D)If 1.5 moles of Al2(CO3)3 are formed, given sufficient starting materials, then 9 moles of NH4NO3 will also be formed.
E)4 moles of Al(NO3)3 will react with 6 moles of (NH4)2CO3.
F)If 4 moles of Al(NO3)3 reacts with 9 moles of (NH4)2CO3 there will be left over (NH4)2CO3
Answers
The incorrect statement regarding the reaction between aqueous solutions of aluminum nitrate, Al(NO3)3, and ammonium carbonate, (NH4)2CO3, which form a precipitate of aluminum carbonate, Al2(CO3)3 is If 0.5 mole of (NH4)2CO3 react with sufficient Al(NO3)3, 3 moles of Al2(CO3)3 will be formed. Option C.
A chemical equation is a description of the chemical reaction that takes place. It contains the formulae of the reactants and products separated by an arrow. The arrow indicates the direction of the reaction. The stoichiometric coefficients in the equation represent the number of moles of each substance involved in the reaction.
Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's important to keep in mind that the law of conservation of mass applies to chemical reactions. This means that the number of atoms of each element present in the reactants must equal the number of atoms of that element present in the products. Thus, stoichiometry plays a significant role in determining how much product is formed from a given amount of reactant and vice versa. Option C.
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for a neutralization reaction, would you expect the magnitude of q to increase, decrease, or stay the same if the concentration of only the acid were doubled? why? group of answer choices increase; if only the concentration of acid were doubled more neutralization reaction would occur because there is more acid than base stay the same; if only the concentration of acid were doubled no additional neutralization reaction would occur decrease; if only the concentration of acid were doubled less neutralization reaction would occur because there is less base than acid
Answers
For a neutralization reaction, more heat is evolved and Q is doubled.
When the concentration of the acid alone is twice in a neutralization process, the value of q (heat of neutralization) is increased twofold. A neutralizing reaction happens when an acid and a base are combined.A neutralization reaction is a reaction in which an acid undergoes a reaction with a base to form salt and water. Ionically, a neutralization reaction goes as follows; H^+(aq) + OH^-(aq) ------> H20(l).The heat of neutralization (Q) of the system depends on the concentration of the solutions. Since Q is dependent on concentration, if the concentration of any of the reactants is doubled, more heat is evolved hence Q is doubled.To learn more about neutralization reaction visit:
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how many moles of gas dpes ot take to occupy 120 liters at a pressure of 2.3 atmospheres and 340k
Answers
The number of moles of gas that occupy a volume of 120 liters at a pressure of 2.3 atmospheres and 340K is 9.88 moles
To solve this, we can use the ideal gas law : PV = nRT
where P = pressure ; V = volume ; n = number of moles ; R = gas constant ; T = temperature ; R = 0.0821 atm L/mol K
Using this formula, we can solve for the number of moles of gas (n) given the other variables :
P = 2.3 atm ; V = 120 L; R = 0.0821 atm L/mol K ; T = 340K
Substituting these values into the equation, we have :
2.3 atm x 120 L = n x 0.0821 atm L/mol K x 340K
n = (2.3 atm x 120 L)/(0.0821 L atm/mol K x 340 K)
n = 9.88 moles
Thus, 9.88 moles of gas are required to occupy a volume of 120 liters at a pressure of 2.3 atmospheres and a temperature of 340K.
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A process which is unfavorable with respect to enthalpy, but favorable with respect to entropy Group of answer choices could occur at high temperatures, but not at lower temperatures. could not occur regardless of temperature. could occur at any temperature. could occur at low temperatures, but not at higher temperatures. none of the above
Answers
Answer:
could occur at any temperature.
Explanation:
The spontaneity of a reaction is what determines whether the reaction will occur or not. A spontaneous reaction occurs easily.
The spontaneity of a reaction is predicted by the sign of ∆G.
When ∆G is positive, the reaction is not spontaneous. When ∆G is negative, the reaction is spontaneous.
Note that;
∆G= ∆H - T∆S
Where;
∆H = Change in enthalpy
∆S = Change in entropy
T= temperature
If ∆H is unfavourable and ∆S is favourable, the reaction can proceed at all temperatures because ∆G will always be negative.
It should be noted that a process that is unfavorable as regards to enthalpy, but favorable with respect to entropy could occur at any temperature.
Enthalpy(∆H) serves as amount of internal energy that a compound has, entropy( ∆S) on the other hand serves as intrinsic disorder within the system.
However, spontaneity of a reaction determines likely hood of occurrence of a reaction, when the process is spontaneous, it makes the reaction to occurs easily.
We can conclude that whenever enthalpy is unfavourable and entropy of a system is favourable, then the spontaneity will be negative and the reaction will occur at any temperature.
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How much space would one mole of grass take up?
Answers
Answer:
If there's a grass area in the shape of a square and one side is 8 metres how much would it cost to fill the grass with fresh gravel at $5/metre
Are the following chemical equations reversible or irreversible?
2H2O ←→ H3O+ + OH-
HA + H2O ←→ A- + H3O+
HA + H2O → A- + H3O+
MOH → M+ + OH-
Answers
The first two chemical equations are reversible while the other two are irreversible.
What are chemical equations?Chemical equation is a symbolic representation of a chemical reaction which is written in the form of symbols and chemical formulas.The reactants are present on the left hand side while the products are present on the right hand side.
A plus sign is present between reactants and products if they are more than one in any case and an arrow is present pointing towards the product side which indicates the direction of the reaction .There are coefficients present next to the chemical symbols and formulas .
The first chemical equation was put forth by Jean Beguin in 1615.By making use of chemical equations the direction of reaction ,state of reactants and products can be stated. In the chemical equations even the temperature to be maintained and catalyst can be mentioned.
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Q-3 Determine the fugacity in atm for pure ethane at 310 K and 20.4 atm and change in the chemical potential between this state and a second state od ethane where temperature is constant but pressure is 24 atm.
Answers
The fugacity in atm for pure ethane at 310 K and 20.4 atm is given by the equation: f = 20.4 exp (-Δg1/RT). The change in chemical potential between this state and a second state of ethane where the temperature is constant but the pressure is 24 atm is -0.0911RT.
Fugacity is a measure of the escaping tendency of a component in a mixture, which is defined as the pressure that the component would have if it obeyed ideal gas laws. It is used as a correction factor in the calculation of equilibrium constants and thermodynamic properties such as chemical potential. Here we need to determine the fugacity in atm for pure ethane at 310 K and 20.4 atm and the change in the chemical potential between this state and a second state of ethane where the temperature is constant but the pressure is 24 atm. So, using the formula of fugacity: f = P.exp(Δu/RT) Where P is the pressure of the system, R is the gas constant, T is the temperature of the system, Δu is the change in chemical potential of the system. Δu = RT ln (f / P)The chemical potential at the initial state can be calculated using the ideal gas equation as: PV = nRT
=> P
= nRT/V
=> 20.4 atm
= nRT/V
=> n/V
= 20.4/RT The chemical potential of the system at the initial state is:
Δu1 = RT ln (f/P)
= RT ln (f/20.4) Also, we know that for a pure substance,
Δu = Δg. So,
Δg1 = Δu1 The change in pressure is 24 atm – 20.4 atm
= 3.6 atm At the second state, the pressure is 24 atm.
Using the ideal gas equation, n/V = 24/RT The chemical potential of the system at the second state is: Δu2 = RT ln (f/24) = RT ln (f/24) The change in chemical potential is Δu2 – Δu1 The change in chemical potential is
Δu2 – Δu1 = RT ln (f/24) – RT ln (f/20.4)
= RT ln [(f/24)/(f/20.4)]
= RT ln (20.4/24)
= - 0.0911 RT Therefore, the fugacity in atm for pure ethane at 310 K and 20.4 atm is:
f = P.exp(Δu/RT)
=> f
= 20.4 exp (-Δu1/RT)
=> f
= 20.4 exp (-Δg1/RT) And, the change in the chemical potential between this state and a second state of ethane where the temperature is constant but pressure is 24 atm is -0.0911RT. Therefore, the fugacity in atm for pure ethane at 310 K and 20.4 atm is given by the equation: f = 20.4 exp (-Δg1/RT). The change in chemical potential between this state and a second state of ethane where the temperature is constant but the pressure is 24 atm is -0.0911RT.
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Is the CO2 content of the atmosphere is as high as 300 parts per million?
Answers
No, the CO2 content of the atmosphere is not as high as 300 parts per million. According to the World Meteorological Organization, the current global average CO2 concentration is around 417 parts per million (ppm).
This is the highest atmospheric CO2 concentration in the last 800,000 years, and it has been steadily increasing since the start of the Industrial Revolution. This increase in atmospheric CO2 is largely due to the burning of fossil fuels, which releases CO2 into the atmosphere. Deforestation and other land use changes also contribute to the release of CO2. The accumulation of CO2 in the atmosphere has caused the global average temperature to rise and has led to climate change. Therefore, a CO2 concentration of 300 ppm is not high enough to cause dangerous climate change, but it is still significantly higher than the pre-industrial level of around 280 ppm.
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Suppose that 25 g of aluminum is initially at 27.0 C. What is the final temperature of aluminum upon absorbing 2,35 kJ of heat? (
c
=
0.903
J
g
.
0
C
)?
Answers
The final temperature of aluminum upon absorbing 2.35 kJ of heat is approximately 130.44 °C.
The heat equation is given by Q = mcΔT, where Q is the heat absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we convert 2.35 kJ of heat to joules: 2.35 kJ × 1000 J/kJ = 2350 J.
Next, we substitute the given values into the heat equation: 2350 J = (25 g) × (0.903 J/g·°C) × ΔT.
Simplifying the equation, we find ΔT = (2350 J) / (25 g × 0.903 J/g·°C) = 103.44 °C.
Finally, we calculate the final temperature by adding the change in temperature to the initial temperature: 27.0 °C + 103.44 °C = 130.44 °C.
Therefore, the final temperature of aluminum upon absorbing 2.35 kJ of heat is approximately 130.44 °C.
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Examine the fossil. List the parts of the animal that you recognize. What kind of animal do you think this was?
Answers
Answer:
I think it was a huge fish. umm not sure
Explanation:
Why do food scientists need to understand chemistry?
A.They study how to make plants produce certain chemicals
B.They use complicated machines to produce food products
C.They use chemicals as flavorings and preservatives
D.They study the effects of different foods on the body
Answers
Answer:
I think it is A
Explanation:
A.They study how to make plants produce certain chemicals
the temperature at which a liquid becomes a gas is called the
Answers
3. Kevin has an unknown element. He wants to find out whether it is a metal or
a non-metal. He heats the substance on one end and the other end gets hot very
quickly. The element is orange in colour and its surface is shiny.
a. Do you think it is a metal or a non-metal?
b. What piece of evidence from the above given information made you decide this?
Explain with respect to the properties of metals and non-metals.
Answers
a) The unknown element that Kevin has is a metal.
Since the unknown element conducts heat, burns with a colored flame, and has a shiny surface- these are the characteristic properties of metals.
b)The piece of evidence that helped to decide was the conduction of heat, orange-colored flame, and shiny surface.
The information provided states that the element is a good conductor of heat as the other end gets heated and burns with an orange-colored flame and also has a shiny surface. These properties confirm that the element is Metal.
Properties of metal-
Metals are good conductors of heat and electricity.Most metals burn with a colored flame.Metals have shiny surfaces.Metals are malleable.Metals are ductile.Properties of non-metal-
Non-metals are poor conductors of heat and electricity.Non-metals do not burn with a colored flame.Non-metals do not have shiny surfaces.Non-metals are not malleable.Non-metals are non-ductile.From the properties stated it is confirmed that the unknown element is a metal.
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How many Sodium (NA) Atoms are in Calcium Oxide
Answers
Answer:
2 Na atoms
Explanation:
when collecting gases over water, the pressure of the pure gas being collected is called the
Answers
The pressure of a pure gas is referred to as the dry gas pressure when gases are being collected over water.
what is dry gas pressure?
It can be challenging to determine the mass of gases because of their low densities. It is usual practise to collect gas over water in order to measure the height of displaced water. To do this, insert a tube into an upside-down bottle whose opening is submerged in a bigger container of water. Dalton's Law must be applied to take water vapor into account when estimating the volume of gas that was collected.
The height of the water displaced in the tube can be used to calculate the overall pressure inside the pneumatic trough device, which is used to collect a gas over water.
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15 pts! Explain how the absorption of energy (heating) affects the speed of the particles in a substance.
Answers
Answer:
See explanation
Explanation:
Temperature has been severally defined as the measure of the average kinetic energy of the molecules of a body. Heat is a form of energy that exists due to temperature difference.
Given a body whose molecules has a speed = (3RT/M)^1/2; this implies that for a given mass of the substance, the velocity of its particles depends on the temperature of the substance.
However, absorption of heat increases the temperature of the body. Therefore, when heat is absorbed, the temperature increases and the speed of the particles of a substance increases according to the relation above.
The conductance of the electric current through the electrolytic solution increases with
a)decrease in dilution
b)increase in dilution
c)increase in concentration
d)low degree of ionization
Answers
The conductance of the electric current through the electrolytic solution increases with increase in concentration.
What is electrolytic solution?
Electrolytic solutions are solutions that are capable of conducting an electric current due to presence of ions.
The current flowing in an Electrolytic solutions is calculated as;
Q = It
I = Q/t
where;
Q is chargesIncrease in the concentration of the charges, increases the amount of charges in the solution and hence the conductance of the solutions will increase as well.
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what is the percentage if one gram is dissolved in 3.0, the specific gravtivty of PEG is 1.12 mL of a solution
Answers
The percentage of the solute in the solution is approximately 29.8%.
The percentage of a solute in a solution can be calculated by dividing the mass of the solute by the mass of the solution, and then multiplying by 100.
In this case, we have 1 gram of solute dissolved in 3.0 mL of a solution. However, the specific gravity of PEG (polyethylene glycol) is given as 1.12 mL of solution per gram of PEG.
To calculate the mass of the solution, we can use the specific gravity. Since 1 gram of PEG occupies 1.12 mL of solution, we can multiply the specific gravity by the volume of the solution:
1.12 mL/g x 3.0 mL = 3.36 grams
Now we can calculate the percentage of the solute:
(1 gram / 3.36 grams) x 100 = 29.8%
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How many grams of potassium chloride can be produced from 356 g of chlorine and 356 g of potassium bromide
Answers
Answer:
223 g
Explanation:
The element with the lowest melting point is: Select one: a. B b. Al c. Ga d. Tl e. All of these have the same melting point.
Answers
The element with the lowest melting point is Ga.
Hence, Option (C) is correct answer.
Melting point is usually defined as the temperature at which solid changes to liquid.
What is the order of melting point of B, Al, Ga, Tl ?The melting point order of B, Al, Ga, Tl is B > Al> Tl > Ga due to structural changes, melting point increases from Ga to Tl. Hence Ga has the lowest melting point among all these.
Thus from the above conclusion we can say that The element with the lowest melting point is Ga.
Hence, Option (C) is correct answer.
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NH3 is a _______________
Answers
Answer:
compound
Explanation:
Answer:
your answer would be compound