Answer to Question #86367 in General Chemistry for Enci Peng

Question #86367
Hydrogen initially occupies 194 liters. If it changes to a volume of 73 L at 0° C and 760 mm Hg. If the initial temperature of the hydrogen was 30° C, what was its initial pressure of the gas in mm Hg? Round to two decimal places.
Expert's answer

Let's denote the parameters of the gas in the initial condition by index 1, and in the final condition by index 2:

@$V_1 = 194~\text{L},~t_1 = 30~\degree\text{C},~P_1 - ?~; \\ V_2 = 73~\text{L},~t_2 = 0~\degree\text{C},~P_2 = 760~\text{mmHg}.@$

We are going to make use Combined gas law for the case when comparing the same substance under two different sets of conditions:

@$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}.@$

For the formula to be correct, the Celsius temperatures should be converted to absolute temperatures (in Kelvin):

@$T = (\frac{t}{\degree\text{C}} + 273.15)~\text{K}; \\ T_1 = (30 + 273.15)~\text{K} = 303.15~\text{K}; \\ T_2 = (0 + 273.15)~\text{K} = 273.15~\text{K}.@$

Solving the Combined gas law for the unknown initial pressure, and entering the numerical values,

@$P_1 = P_2\frac{V_2}{T_2}\frac{T_1}{V_1} = 760~\text{mmHg}~*~\frac{73~\cancel{\text{L}}}{273.15~\cancel{\text{K}}}~*~\frac{303.15~\cancel{\text{K}}}{194~\cancel{\text{L}}} \approx 317.39~\text{mmHg}.@$

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