general chemistry chapter 6

Question

Suppose a boil water notice is sent out advising all residents in the area to boil their water before drinking it or using it for cooking. You need to boil 19.0 L of water using your natural gas (primarily methane) stove. What volume of natural gas is needed to boil the water if only 17.2% of the heat generated goes towards heating the water. Assume the density of methane is 0.668g/L ,the density of water is 1.00 g/ml, and that the water has an initial temperature of 21.1 degrees c. Enthalpy of formation values can be found in this. Assume that gaseous water is formed in the combustion of methane.

Answer 1

Hello, Sarah,

Please add key information such as the heat of vaporization and specific heat of water, and the enthalpy of combustion for methane to problems such as these. The book values may differ from the values others may have access to. (And it takes more time to help).

The energy required to boil water involves 3 key steps. We need the energies of:

1. bringing 19L of water from 21.1C to 100C,
2. vaporizing 19L of 100C water, and we need
3. the energy released by methane combustion

The values I'll use for each step are based on a web search, so adjust accordingly if they differ from the ones you've been given.

1. Bring 19000 grams of water to 100C from 21.1C

(19000g)*(4.184J/gC)(100C-21.1C) = 6272234 J or 6272 kJ

2. Vaporize the water

(19kg)*(2260kJ/kg) = 42940 kJ

This is a total of 49,212 kg of energy

3. We need to divide this number by the efficiency, 0.172, to account for heat loss. That means we need 286,120 kJ of methane combustion.

4. Methane's heat of combustion is 55.51 kJ/g . (286,120 kJ)/(55.51kJ/g) = 5154 grams of methane.

5. Divide by the density of methane to find the liters of metane that contain this amount of energy. I get

7,720 liters.

Bob