A typical bathtub can hold 106 gallons of

Question

water. Calculate the mass of natural gas that
would need to be burned to heat the water
for a tub of this size from 56 ◦F to 87 ◦F.
Assume that the natural gas is pure methane
(CH4) and that the products of combustion
are carbon dioxide and water (liquid).
Answer in units of g

2nd part
What volume of natural gas does this correspond to at 30◦C and 1 atm?
Answer in units of L

Answer 1

a.
1. Convert F to C. Convert 106 gallons H2O to L, assume density of 1.0 g/mL and convert L to grams.
2. Calculate q = heat required to heat the water as described.
q = mass H2O x specific heat H2O x (Tfinal - Tinitial).

3. Write and balance the equation for the combustion of CH4.
CH4 + 2O2 ==> CO2 + 2H2O

4. Calculate heat of combustion.
dHfrxn from step 2 = (n*dHf products) - (n*dHf reactants). Call this dHrxn

5. dHrxn in kJ/16g CH4 x # g CH4 = q
Solve for #g CH4

Check my thinking.

b.
Use PV = nRT and solve for V in L. You will need to plug in for n; remember n = grams/molar mass. You know g and molar mass so you can calculate n and obtain V from there.