Question

a gas has a temperature of 310 k and a pressure of 101 kpa. find the volume occupied by 1.25 mol of this gas, assuming it is ideal.
a. 0.097 m³
b. 0.065 m³
c. 0.032 m³
d. 0.071 m³
e. 0.012 m³

Explanation:

Step1: Recall ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal - gas constant ($R=8.31\ J/(mol\cdot K)$), and $T$ is temperature. We need to solve for $V$.

Step2: Rearrange the ideal - gas law formula

Rearranging $PV = nRT$ for $V$ gives $V=\frac{nRT}{P}$.

Step3: Substitute the given values

We have $n = 1.25\ mol$, $R = 8.31\ J/(mol\cdot K)$, $T = 310\ K$, and $P=101\times10^{3}\ Pa$.
\[

$$\begin{align*} V&=\frac{1.25\ mol\times8.31\ J/(mol\cdot K)\times310\ K}{101\times 10^{3}\ Pa}\\ &=\frac{1.25\times8.31\times310}{101\times 10^{3}}\ m^{3}\\ &=\frac{1.25\times8.31\times310}{101000}\ m^{3}\\ &=\frac{3207.375}{101000}\ m^{3}\\ &\approx0.032\ m^{3} \end{align*}$$

\]

Answer:

C. $0.032\ m^{3}$