Question

How many kilograms of water at 15oC can be heated to 95oC by burning 143 grams of methane, CH4, assuming that 100% of the heat is used to heat the water. The heat of combustion of methane is 891 kJ per mole of methane. (The specific heat of water is 4.184 J/goC.)

Answer 1

23.7 kg is the mass of H₂O that can be heated

Step-by-step explanation:

First of all, we need to determine the heat used.

891 kJ per mol of methane is released in the combustion, but we don't have 1 mol, we have 143 g

We convert the mass to moles → 143 g . 1mol / 16 g = 8.93 moles

Now, a rule of three:

1 mol of CH₄ release a heat of 891 kJ

8.93 moles of CH₄ will release (8.93 . 891 kJ) / 1 = 7956.63 kJ

If we convert to J → 7956.63 kJ . 1000 J / kJ = 7956630 Joules

Now we determined the heat released, we can apply the calorimetry formula

Q = m . C . (Final T° - Initial T°)

7956630 J = mass . 4.184 J/g°C ( 95°C - 15°C)

7956630 J / 4.184 J/g°C . 80°C = mass

23771 g = mass

If we convert from g to kg → 23771 g . 1kg / 1000 g = 23.7 kg