# Question afa15

Dec 16, 2015

$\text{31 mL}$

#### Explanation:

Your tool of choice for any ideal gas problem will always be the ideal gas law equation. You can derive any other gas equation by using the ideal gas law equation, so always start with that in mind.

So, your sample of nitrogen gas, ${\text{N}}_{2}$, goes from a volume of $\text{30.0 mL}$, a temperature of ${25}^{\circ} \text{C}$, and a pressure of $\text{730 mmHg}$, to a temperature of ${50}^{\circ} \text{C}$ and a pressure of $\text{1 atm}$.

This tells you that you can use the ideal gas law equation to describe the two states of the gas

${P}_{1} \cdot {V}_{1} = n \cdot R \cdot {T}_{1} \to$ for the initial state

${P}_{2} \cdot {V}_{2} = n \cdot R \cdot {T}_{2} \to$ for the final state

Notice that you can divide these equations to get

$\frac{{P}_{1} \cdot {V}_{1}}{{P}_{2} \cdot {V}_{2}} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{n \cdot R}}} \cdot {T}_{1}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{n \cdot R}}} \cdot {T}_{2}}$

This is equivalent to

$\frac{{P}_{1} {V}_{1}}{T} _ 1 = \frac{{P}_{2} {V}_{2}}{T} _ 2 \to$ the combined gas law equation

Now all you have to do is plug in your values and solve for ${V}_{2}$. Do not forget to convert the pressure from mmHg to atm and the temperature from degrees Celsius to Kelvin!

$\text{1 atm " = " 760 mmHg}$

This will get you

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

V_2 = (730/760color(red)(cancel(color(black)("atm"))))/(1color(red)(cancel(color(black)("atm")))) * ( (273.15 + 50)color(red)(cancel(color(black)("K"))))/( (273.15 + 25)color(red)(cancel(color(black)("K")))) * "30.0 mL" = "31.23 mL"#

You should round this off to one sig fig, but I'll leave it rounded to two sig figs

${V}_{2} = \textcolor{g r e e n}{\text{31 mL}}$