Question

1. A sample of nitrogen gas occupies a volume of 8.98 L at 51 °C and 0.4560 atm. If the volume of the gas sample is increased to 11100 mL, while its temperature is decreased to -1 °C, the resulting gas pressure, in torr, will be___ torr.

2. A sample of methane gas collected at a pressure of 226 mm Hg and a temperature of 286 K has a mass of 20.1 grams. The volume of the sample is __L.

Answer 1

Problem 1.

Let's use ideal gas law

$$pV = \nu RT$$

where $R \approx 8.314[{{\rm{J}} \over {{\rm{K}} \cdot {\rm{mol}}}}]$ - universal gas constant and $\nu$ is the amount of moles. Using this law for the first and the second state we get

$${p_1}{V_1} = \nu R{T_1}$$ $${p_2}{V_2} = \nu R{T_2}$$

Divide the second by the first

$${{{p_2}{V_2}} \over {{p_1}{V_1}}} = {{{T_2}} \over {{T_1}}}$$

and for the pressure at the second state

$${p_2} = {p_1}{{{V_1}} \over {{V_2}}}{{{T_2}} \over {{T_1}}}$$

Let's do the calculations using that $T[K] = T[^\circ C] + 273.15$ and $1[{\rm{atm}}] = 760[{\rm{torr}}]$

$${p_2} = 0.456[{\rm{atm}}]{{9.98[{\rm{L}}]} \over {11100 \cdot {{10}^{ - 3}}[{\rm{L}}]}}{{272.15[{\rm{K}}]} \over {324.15[{\rm{K}}]}} \approx 0.3442[{\rm{atm}}] \approx 261.592[{\rm{torr}}]$$

Problem 2.

Let's use the ideal gas law again

$$pV = \nu RT$$

Methane has the chemical formula $C{H_4}$ and has the molar mass ${M_{C{H_4}}} \approx 16.043[{{\rm{g}} \over {{\rm{mol}}}}]$. The number of moles can be found as $\nu = {m \over M}$ , thus

$$V = {1 \over p}{m \over {{M_{C{H_4}}}}}RT$$

Let's do the calculations using that $1[{\rm{mmHg}}] \approx 133.322[{\rm{Pa}}]$

$$V = {1 \over {226 \cdot 133.322[{\rm{Pa}}]}}{{20.1[{\rm{g}}]} \over {16.043[{{\rm{g}} \over {{\rm{mol}}}}]}}8.314[{{\rm{J}} \over {{\rm{K}} \cdot {\rm{mol}}}}] \cdot 286[{\rm{K}}] \approx 0.0989[{{\rm{m}}^3}] \approx 98.87[{\rm{L}}]$$