What is the total pressure (mmHg) of a gaseous mixture of 3.7 g of hydrogen gas and 9.1 g of oxygen gas in a 3.24-L flask if the partial pressure of hydrogen is 318 mmHg?

Question

Natalie Anton · Accepted Answer

Approx. #1.5*atm#.

In the presence of constant temperature and volume, which are both present here despite our ignorance of their exact values, pressure is directly related to the moles of gas present, or vice versa. #"Moles of dihydrogen"# #=# #(3.7*g)/(2.02*g*mol^-1)=1.83*mol#. #"Moles of dioxygen"# #=# #(9.1*g)/(32.00*g*mol^-1)=4.97*mol#. We are given that #P_"dihydrogen"=318*mm*Hg=(318*mm*Hg)/(760*mm*Hg*atm^-1)=0.418*atm# Furthermore, considering the relationship between pressure and moles, #P_"dioxygen"=(4.97*mol)/(1.83*mol)xx0.418*atm=1.135*atm#. And finally, #P_"Total"=P_"dihydrogen"+P_"dioxygen"# #=# #(0.418+1.135)*atm# Note that I converted the #mm*Hg# to units of #"atmospheres"#, because I really don't think #mm*Hg# should be used for pressures much above #1*atm, i.e. 760*mm*Hg#. There seems to be quite a few questions on these boards where mercury columns greater than #760*mm*Hg# have been used to measure pressure. Obviously, the person who set the question has never had to clean up a mercury spill.

Ellie Andrews · Answer

undefined To find the total pressure of the gaseous mixture, we need to first calculate the partial pressure of oxygen gas using the given information and then add it to the partial pressure of hydrogen gas.

We can use the ideal gas law equation:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = gas constant (0.0821 atm·L/mol·K)
T = temperature (in Kelvin)

First, we need to convert the given masses of hydrogen and oxygen gas to moles using their molar masses:

Molar mass of hydrogen (H2) = 2.02 g/mol
Molar mass of oxygen (O2) = 32.00 g/mol

Next, we use the formula:

n = mass / molar mass

Then, we can calculate the partial pressure of oxygen gas (PO2) using Dalton's law of partial pressures:

PO2 = (mass of O2 / molar mass of O2) * RT / V

Finally, we find the total pressure by adding the partial pressures of hydrogen and oxygen:

Total pressure = PH2 + PO2