Question 12.7: Calculating Final Volume of a Gas Using the Combined Gas Law......
Calculating Final Volume of a Gas Using the Combined Gas Law
Hydrogen gas (H _2 ) is the least dense of all gases. A sample of H _2 gas is found to occupy a volume of 1.23 L at 755 mm Hg and 0°C. What volume, in liters, will this same gas sample occupy at 735 mm Hg pressure and a temperature of 50°C?
Writing all the given data in the form of initial and final conditions, we have
P_1 = 755 mm Hg P_2 = 735 mm Hg
V_1 = 1.23 L V_2 = ?L
T_1 = 0°C = 273 K T_2 = 50°C = 323 K
Rearrangement of the combined gas law expression to isolate V_2 on the left side gives
V_2 =V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}Substituting numerical values into this equation and doing the arithmetic gives
V_2 =1.23 \textrm{ L} \times \frac{755 \cancel{\textrm{mm Hg}}}{735 \cancel{\textrm{mm Hg}}} \times \frac{323 \textrm{ K}}{273 \textrm{ K}}= 1.494874 L (calculator answer)
= 1.49 L (correct answer)
Answer Double Check: Is the setup for solving the problem reasonable? Yes. The original volume, V_1 , is multiplied by a pressure factor and a temperature factor. The pressure factor has a value greater than one because volume increases with a decrease in pressure. The temperature factor also has a value greater than one because volume increases as temperature increases.