Question

a reaction at 9.0°c evolves 780 mmol of dinitrogen monoxide gas
calculate the volume of dinitrogen monoxide gas that is collected. you can assume the pressure in the room is exactly 1 atm. be sure your answer has the
correct number of significant digits

Explanation:

Step1: Convert units

Convert temperature to Kelvin: $T=(9.0 + 273.15)\text{ K}=282.15\text{ K}$. Convert moles: $n = 780\text{ mmol}=0.78\text{ mol}$.

Step2: Use ideal gas law

The ideal gas law is $PV = nRT$. Here, $P = 1\text{ atm}$, $R=0.0821\text{ L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$. Rearrange for $V$: $V=\frac{nRT}{P}$.
Substitute values: $V=\frac{0.78\text{ mol}\times0.0821\text{ L}\cdot\text{atm}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}\times282.15\text{ K}}{1\text{ atm}}$.
Calculate: $V = 0.78\times0.0821\times282.15\text{ L}\approx18\text{ L}$.

Answer:

$18\text{ L}$