A household water heater containing 50 gallons (227 L) of water is heated burning natural gas (methane, molar mass = 16.043 g mol-1) via the following reaction: CH4(g) + O2(g) → CO2(g) + H20() A,H = -891 kJ mol-1 What mass of methane, in units of g, is needed to heat the 227 L of water in the heater from 25.0°C to 44.0°C? Assume: • the heater is 100% efficient in its use of heat energy • no heat is lost to the surroundings • specific heat of water is: 4.184 J g-1 °C-1 • density of water is: 0.9970 g mL¯1

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A household water heater containing 50 gallons (227 L) of water is heated burning
natural gas (methane, molar mass = 16.043 g mol-1) via the following reaction:
CH4(g) + O2(g)
CO2(g) + H20(O
A,H = -891 kJ mol-1
What mass of methane, in units of g, is needed to heat the 227 L of water in the
heater from 25.0°C to 44.0°C?
Assume:
• the heater is 100% efficient in its use of heat energy
• no heat is lost to the surroundings
specific heat of water is: 4.184 Jg-1 °C-1
density of water is: 0.9970 g mL¯1
Transcribed Image Text:A household water heater containing 50 gallons (227 L) of water is heated burning natural gas (methane, molar mass = 16.043 g mol-1) via the following reaction: CH4(g) + O2(g) CO2(g) + H20(O A,H = -891 kJ mol-1 What mass of methane, in units of g, is needed to heat the 227 L of water in the heater from 25.0°C to 44.0°C? Assume: • the heater is 100% efficient in its use of heat energy • no heat is lost to the surroundings specific heat of water is: 4.184 Jg-1 °C-1 density of water is: 0.9970 g mL¯1
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