Question

The volume of a gas is 200.0 mL at 275 K and 92.1 kPa. Find its volume at STP.

Answer 1

To solve this question we will use ideal gas equation:
$p*V=n*R*T$
Where:
p = pressure
V = volume
n = number of moles
R = gas constant
T = temperature

We can rearrange formula to get:
$\frac{p*V}{T} =n*R$
We are working woth same gas so we can write following formula. Index 1 stands for conditions before change and index 2 stands for conditions after change.
$\frac{ p_{1}*V_{1} }{T_{1}} = \frac{ p_{2}*V_{2} }{T_{2}}$

We are given:
p1=92.1kPa = 92100Pa
V1=200mL = 0.2L
T1=275K
p2= 101325Pa
T2=273K
V2=?

We start by rearranging formula for V2. After that we can insert numbers:
${ p_{1}*V_{1} *T_{2}} = { p_{2}*V_{2}*T_{1} } \\ \\ V_{2}= \frac{p_{1}*V_{1} *T_{2}}{ p_{2}*T_{1}} \\ \\ V_{2}= \frac{92100*0.2*273}{101325*275} \\ \\ V_{2}= 0.18L=180mL$