# Question 5e940

Jan 29, 2016

Here's what I got.

#### Explanation:

Since your didn't provide enough information to allow for a direct answer, I'll try to take a more general approach and show you how to solve similar problems in the future.

Your tool of choice for any ideal gas problem is the ideal gas law equation. You can use it to derive all the other gas law equation.

$\textcolor{b l u e}{P V = n R T} \text{ }$, where

$P$ - the pressure of the gas
$V$ - the volume it occupies
$n$ - the number of moles of gas
$R$ - the universal gas constant, usually given as $0.0821 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - the absolute temperature of the gas, i.e. the temperature expressed in Kelvin.

Now, the problem starts like this

A sample of ammonia gas in a non-rigid container occupies a volume of $\text{4.00 L}$ at a certain temperature and pressure.

This tells you two important things

• the number of moles of gas is probably constant
• the volume of the gas is not constant

We can now distinguish three possible scenarios

• Pressure and temperature change

Let's say that the ammonia gas is initially kept at a pressure ${P}_{1}$ and a temperature ${T}_{1}$. If the number of moles of gas is indeed kept constant, you can rearrange the ideal gas law equation to get

$P V = n R T \implies \frac{P V}{T} = {\overbrace{n \cdot R}}^{\textcolor{g r e e n}{\text{constant}}}$

This means that you can equate the initial state of the gas with a final state by writing

$\textcolor{b l u e}{\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2} \to$ the combined gas law equation

This equation implies that both the temperature and the pressure of the gas change from ${T}_{1}$ and ${P}_{1}$, respectively, to ${T}_{2}$ and ${P}_{2}$.

To get the new volume of the gas, rearrange this equation to solve for ${V}_{2}$

${V}_{2} = {P}_{1} / {P}_{2} \cdot {T}_{2} / {T}_{1} \cdot {V}_{1}$

At this point, you would use the new values for pressure and temperature, ${P}_{2}$ and ${T}_{2}$, respectively, to find the new volume.

• Pressure changes, but temperature remains constant

Once again, start from the ideal gas law equation. This time the pressure of the gas changes, but its temperature is kept constant.

$P V = {\overbrace{n \cdot R \cdot T}}^{\textcolor{g r e e n}{\text{constant}}}$

You will thus have

color(blue)(P_1V_1 = P_2V_2 -># the equation for Boyle's Law

This time, the new volume of the gas will be

${V}_{2} = {P}_{1} / {P}_{2} \cdot {V}_{1}$

Finally, the third possible scenario

• Pressure is kept constant, but temperature changes

Starting from the ideal gas law equation

$P V = n R T \implies \frac{V}{T} = {\overbrace{\frac{n R}{P}}}^{\textcolor{g r e e n}{\text{constant}}}$

You will thus have

$\textcolor{b l u e}{{V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}} \to$ the equation for Charles' Law

This time, the new volume of the gas will be

${V}_{2} = {T}_{2} / {T}_{1} \cdot {V}_{1}$

This is how you can figure out which gas law to use. Remember, the ideal gas law equation can be used as the starting point for all of them.