Question

Two flasks of equal volume and at the same temperature contain different gases. One flask contains 5.0 g of O2, and the other flask contains 5.0 g of H2. Is each of the following statements true or false? Explain.
a) True. Because the gases have the same volumes, they must have the same number of molecules.
b) False. Because the molar mass of O2 is greater than the molar mass of H2, 5.0g of O2 will contain fewer molecules than 5.0 g of H2.
c)False. Depending on the pressure each flask may contain different numbers of molecules.

Answer 1

Explanation:

• The relationship of number of moles and volume at constant temperature and pressure was given by Avogadro's law.

This law states that volume is directly proportional to number of moles at constant temperature and pressure.

Mathematically,    $V \propto n$

As the given gases have same volume so they will have same number of moles.

Hence, the statement gases have the same volumes, they must have the same number of molecules, is true.

• As number of molecules present in a gas depends on the number of moles present in it. And, number of moles vary with the molar mass of a substance.

 No. of moles of $O_{2}$ = $\frac{mass}{\text{molar mass}}$

                               = $\frac{5.0 g}{32 g/mol}$

                               = 0.156 mol

Hence, no. of molecules of $O_{2}$ = $0.156 \times 6.022 \times 10^{23}$

                              = $0.94 \times 10^{23}$ molecules

No. of moles of $H_{2}$ = $\frac{mass}{\text{molar mass}}$

                               = $\frac{5.0 g}{2 g/mol}$

                               = 2.5 mol

Hence, no. of molecules of $H_{2}$ = $2.5 mol \times 6.022 \times 10^{23}$

                              = $15.05 \times 10^{23}$ molecules

As, molar mass of oxygen gas is different as compared to the molar mass of hydrogen gas. Therefore, the statement 5.0 g of $O_{2} will contain same molecules as 5.0 g of [tex]H_{2}$ is not true.

• Boyle's Law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.

                 $P\propto \frac{1}{V}$     (at constant temperature and number of moles)

Therefore, when volume of both the gases is same then pressure should also be the same.

Hence, the statement depending on the pressure each flask may contain different numbers of molecules, is false.