A hot water heater uses natural gas as a fuel. What mass of natural gas must be completely combusted to
raise the temperature of 46.3 litres of water by 35.0'C ? Assume 100% of the energy released by the
combustion of natural gas is absorbed by the water. (Value: 5 points)

 

Assuming that the natural gas is primary consist of methane (CH₄), then you need at least 122.14 g of natural gas to be completely combusted in order to raise the temperature of the given volume of water up to desired temperature.

See explanation for complete solutions.

Step-by-step explanation

CONCEPTS:

In this scenario, a given volume of water is using natural gas for heating. The process needs that a natural gas to be completely combusted and then the heat released from combustion will be used to heat up or increase the temperature of water.

Heat_{released by combustion} = Heat_{absorbed by water}

To solve this problem we need to determine first the heat that will be needed to absorb by the water to increase its temperature by 35 ^oC. The equation for calculating the heat change is given by:

q = msΔT

where,

q= amount of heat absorbed/released

m= mass of substance

s = specific heat of substance

ΔT = T_final - T_initial = temperature change

GIVEN:

V_water = 46.3 L = 46300 mL

ΔT = 35 ^oC

s_water = 4.184 J/g.^oC

SOLUTION:

Convert the given volume of water to mass using its density.

density of water = 1 g/mL

mass, m of water = 46300 mL X (1g/mL)

m = 46300 g

Determine the heat needed to be absorbed by water.

q = msΔT

q = (46300 g) (4.184 J/g.^oC)(35 ^oC)

q = 6,780,172 J or 6780 kJ

Since we already have the amount of heat needed to be absorbed, we can now equate this to the amount of heat that should be released during combustion and find the mass of natural gas that will be needed

Assuming the given natural gas is primarily consist of methane, CH₄. The combustion reaction is represented by the chemical equation below.

CH_4(g) + 2O_2(g) ---> CO_2(g) + 2H₂O_(l) ΔH = -890.4 kJ/mol

In this reaction, the heat released based on literature values is equals to 890.4 kJ/mol or 55.51 kJ/g

Heat_released = 55.51 kJ/g

Heat_{released by combustion} X mass of natural gas = Heat_{absorbed by water}

(55.51 kJ/g) (mass of natural gas) = 6780 kJ

mass of natural gas = 122.14 g