A pressure of 1.0 x 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 = 0.082 1 L*atm/mol*K,and N_A = 6.02 x 10²³) A)16 x 10¹⁸ B)4.7 x 10¹⁶ C)3.3 x 10¹² D)3.4 x 10⁹

Question

Quizplus · Accepted Answer

First, convert the pressure to atm:

P = 1.0 x 10^-11 mmHg / (760 mmHg/atm) = 1.316 x 10^-17 atm

Next, use the Ideal Gas Law to calculate the number of molecules:

PV = nRT

n/V = P/RT = (1.316 x 10^-17 atm) / (0.0821 L*atm/(mol*K) * 293 K) = 5.96 x 10^-22 mol/L

Finally, convert the number of moles to number of molecules:

N = n*N_A = (5.96 x 10^-22 mol/L) * (6.02 x 10^23 molecules/mol) = 3.58 x 10^2 molecules/L

Round to 3 significant figures gives 3.30 x 10^12 molecules/L or 3.3 x 10^12 molecules/L. Hence, the answer is option C.

A Pressure of 1