Chemistry Gas Laws Hw help!!

Question

A gas had a volume of 43.5L and 3.69mol. What do you think the final volume of the gas would be if the number of moles decreased to 1.22mol at constant temperature and pressure? What is the name of the law used?

A gas had an initial moles of 2.31mol when the volume was 25.6L. Calculate the new moles if the volume of the gas increased to 33.5L at constant temperature and pressure. Name the law used.

Answer 1

Hello, Mar,

In both cases the law I used was the Ideal Gas Law. Other gas laws include:

1. Boyle’s Law
2. Charles' Law
3. Gay-Lussac’s Law

None of these accounts for a change in number of moles of gas. The ideal gas law is:

PV = nRT,

where:

P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. The units of P and V can be whatever is convenient (LO, ml, cm³, atm, mmHg, bar, etc.) as long as they are consistent in the problem AND if the gas constant, R, is chosen with the same units, so that they cancel properly. This law is derived from the first three laws. The temperature must always be Kelvin.

For both questions, we can use the ideal gas law and calculate the change in the unit that is unknown.

The first question asks for the change in volume when the amount of gas is decreased with constant temperature(T) and pressure(P).

If we use the subscripts 1 and 2 for initial and final conditions, we can write two equations for both conditions:

P₁V₁ = n₁RT₁, and

P₂V₂ = n₂RT₂

Divide the two:

(P₁V₁)/(P₂V₂) = (n₁RT₁)/(n₂RT₂)

The gas constant, R, cancels out and in the first question, both T and P are constant, so they also cancel out to give:

V1/V2 = n₁/n₂

Since we want V₂, rearrange for V₂: V₂ = V₁*(n₂/n₁)

This tells us that in we increase the number of moles, with everything but volume constant, we'll see a corresponding increase in volume. Makes sense to me.

Using the same logic, we can rearrange the same equation to find n₂, since that is the variable in the second part.

Use those relationships to find V₂ for the first question and n₂ for the second.

Bob

Answer 2

The name of the law is Avogadro's law. It can be expressed as V1/n1 = V2/n2

V1 = initial volume = 43.5 L

n1 = initial moles = 3.69 mol

V2 = final volume = ?

n2 = 1.22 mol

43.5/3.69 = V2/1.22 and V2 = final volume = 14.4 L

n1 = initial moles = 2.31

V1 = initial volume = 25.6 L

n2 = final moles = ?

V2 = final volume = 33.5 L

Again, since temperature and pressure are constant, this is Avogadro's law. Solve as above. Just plug in the values and solve for n2.