# The STP volume of an ideal gas is 2.78 m^3. What is the pressure of the sample at 1.75 m^3 and 27°C?

Dec 22, 2015

${P}_{2} = 1.75 a t m$

#### Explanation:

The initial conditions are:
STP means: ${T}_{1} = 273 K$ and ${P}_{1} = 1 a t m$
The volume of the gas is ${V}_{1} = 2.78 {m}^{3}$

Since the volume (${V}_{2} = 1.75 {m}^{3}$) and temperature (${T}_{2} = 300 K$) are changing at the same time, the new pressure could be found using:

$\frac{{P}_{1} {V}_{1}}{{T}_{1}} = \frac{{P}_{2} {V}_{2}}{{T}_{2}}$

$\implies {P}_{2} = \frac{{P}_{1} {V}_{1}}{{T}_{1}} \times \frac{{T}_{2}}{{V}_{2}} = \frac{1 a t m \times 2.78 \cancel{{m}^{3}}}{273 \cancel{K}} \times \frac{300 \cancel{K}}{1.75 \cancel{{m}^{3}}} = 1.75 a t m$