Question 12.19: Calculating the Molar Volume of a Gas What is the molar volu......

As in the previous example, the ideal gas law, rearranged in the form in which volume is isolated on the left side of the equation, is used to do each of the calculations. The temperature, pressure, and number of moles (1 mole by definition) are known. Note that the chemical formula of the gas does not enter into the calculation as there is nothing in the ideal gas law equation that relates specifically to a gas’s chemical identity. This means that the calculation in each part will be identical. All gases at a given temperature and pressure will have the same molar volume as is shown in this set of calculations.

a. molar volume of H _2 (V) = \frac{nRT}{P} = \frac{(1  \cancel{\textrm{mole}}) \Bigl( 0.08206  \frac{\cancel{\textrm{atm}} \cdot \textrm{L}}{ \cancel{\textrm{mole}} \cdot \cancel{\textrm{K}}} \Bigr) (298  \cancel{\textrm{K}})}{(0.673  \cancel{\textrm{atm}})}

= 36.335631 L H _2      (calculator answer)
= 36.3 L H _2               (correct answer)

b. molar volume of He (V) = \frac{nRT}{P} = \frac{(1  \cancel{\textrm{mole}}) \Bigl( 0.08206  \frac{\cancel{\textrm{atm}} \cdot \textrm{L}}{ \cancel{\textrm{mole}} \cdot \cancel{\textrm{K}}} \Bigr) (298  \cancel{\textrm{K}})}{(0.673  \cancel{\textrm{atm}})}

= 36.335631 L He     (calculator answer)
= 36.3 L He               (correct answer)

c. molar volume of CO (V) = \frac{nRT}{P} = \frac{(1  \cancel{\textrm{mole}}) \Bigl( 0.08206  \frac{\cancel{\textrm{atm}} \cdot \textrm{L}}{ \cancel{\textrm{mole}} \cdot \cancel{\textrm{K}}} \Bigr) (298  \cancel{\textrm{K}})}{(0.673  \cancel{\textrm{atm}})}

= 36.335631 L CO     (calculator answer)
= 36.3 L CO               (correct answer)

d. molar volume of HCN (V) = \frac{nRT}{P} = \frac{(1  \cancel{\textrm{mole}}) \Bigl( 0.08206  \frac{\cancel{\textrm{atm}} \cdot \textrm{L}}{ \cancel{\textrm{mole}} \cdot \cancel{\textrm{K}}} \Bigr) (298  \cancel{\textrm{K}})}{(0.673  \cancel{\textrm{atm}})}

= 36.335631 L HCN     (calculator answer)
= 36.3 L HCN               (correct answer)

Answer Double Check: Different gaseous substances at the same temperature and pressure should have the same molar volume. Thus, answers to all parts of this example should be the same. Such is the case.