Question

A gas sample contains 16.0 g of CH4, 16.0 g of O2, 16.0 g of SO2, and 33.0 g of CO2. What is the total number of moles of gas in the sample? :
A) 2.50 moles
B) 3.00 moles
C) 2.75 moles
D) 2.25 moles
E) 4.00 moles

Answer 1

The answer is A) 2.50 moles

Atomic masses (A) of the following atoms are:
A(C) = 12 g/mol
A(O) = 16 g/mol
A(H) = 1 g/mol
A(S) = 32 g/mol

The number of moles (n) is the quotient of mass (m) and molar mass (M)
n = m/M

m(CH4) = 16.0 g
M(CH4) = A(C) + 4A(H)= 12 + 4 * 1 = 12 + 4 = 16 g/mol
n(CH4) = 16.0 g / 16 g/mol = 1 mol

m(O2) = 16.0 g
M(O2) = 2A(O) = 2 * 16 = 32 g/mol
n(O2) = 16.0 g / 32 g/mol = 0.5 mol

m(SO2) = 16.0 g
M(SO2) = A(S) + 2A(O)= 32 + 2 * 16 = 32 + 32 = 64 g/mol
n(SO2) = 16.0 g / 64 g/mol = 0.25 mol

m(CO2) = 33.0 g
M(CO2) = A(C) + 2A(O)= 12+ 2 * 16 = 12 + 32 = 44 g/mol
n(CO2) = 33.0 g / 44 g/mol = 0.75 mol

The total number of moles of gas in the sample is:
n(CH4) + n(O2) + n(SO2) + n(CO2) = 1 mol + 0.5 mol + 0.25 mol + 0.75 mol =
= 2.50 moles