A pressure of 3.00 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 298 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

Question

Quizplus · Accepted Answer

First, we need to convert the pressure from mmHg to atm:
3.00 × 10^-17 mmHg = 3.00 × 10^-17/760 atm = 3.95 × 10^-20 atm

Next, we can use the ideal gas law to solve for the number of gas molecules:
PV = nRT
n = PV/RT
n = (3.95 × 10^-20 atm)(1 L)/(0.082 L·atm/mol·K)(298 K)
n = 1.62 × 10^-22 mol

Finally, we can convert from moles to molecules:
1 mol = 6.02 × 10^23 molecules
1.62 × 10^-22 mol = 9.75 × 10^1 molecules

Therefore, the number of gas molecules per liter volume is 9.75 × 10^12, which corresponds to choice C.

A Pressure of 3