A pressure of 2.0 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 293 K? (760 mm of Hg = 1 atm,R = 0.0821 L · atm/mol · K,and N_A = 6.02 × 10²³)

Question

Quizplus · Accepted Answer

Using the ideal gas law, PV = nRT, we can find the number of moles (n) and then multiply by Avogadro's number (N_A) to find the number of molecules. Converting pressure to atm: 2.0 × 10⁻⁷ mm Hg × (1 atm / 760 mm Hg) = 2.63 × 10⁻¹⁰ atm. Then, n = PV/RT = (2.63 × 10⁻¹⁰ atm × 1 L) / (0.0821 L·atm/mol·K × 293 K) = 1.09 × 10⁻¹² mol. Finally, molecules = n × N_A = 1.09 × 10⁻¹² mol × 6.02 × 10²³ molecules/mol = 6.6 × 10¹¹ molecules, which matches option B when considering significant figures.

A Pressure of 2