How do you calculate the number of mol of a gas that is present in a 5.67 L container at 44.7 C, if the gas exerts a pressure of 614.0 mmHg.?

Question

Wyatt Atkins · Accepted Answer

#n=(PV)/(RT)# #~=0.17*mol# #n=(PV)/(RT)# #=# #(((614*mm*Hg)/(760*mm*Hg*atm^-1)xx5.67*L))/(0.0821*L*atm*K^-1*mol^-1xx317.9*K)# #~=0.17*mol# This simply an application of the Ideal Gas Equation. Units of pressure are always a problem, because these units dictate the choice of gas constant, #R#. The most convenient unit of pressure is still the #"atmosphere"#, and this is a unit that is very intuitive. Given this, most chemists would use #mm*Hg#, knowing that #760*mm*Hg-=1*atm#, or rather that #1# #atm# of pressure will support a column of mercury that is #760*mm# high. And thus conversion of #mm*Hg# to #"atmospheres"# makes the choice of gas constant easy.

Caleb Adams · Answer

undefined To calculate the number of moles of gas, you can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, convert the temperature from Celsius to Kelvin: 44.7°C + 273.15 = 317.85 K

Then, plug in the values:
P = 614.0 mmHg
V = 5.67 L
T = 317.85 K

The gas constant R is 0.0821 L·atm/(K·mol).

Now solve for n:
n = (P * V) / (R * T)

Substitute the values:
n = (614.0 mmHg * 5.67 L) / (0.0821 L·atm/(K·mol) * 317.85 K)

Calculate:
n ≈ (3484.38 mmHg * L) / (25.98 L·mmHg/(K·mol))
n ≈ 134.18 mol