Final answer:
The kg of water heated using the heat of combustion of ethane, convert the energy from kJ to J and use q = mcΔT, where q is the energy from combustion, m is the mass, c is the specific heat capacity of water, and ΔT is the change in temperature.
Step-by-step explanation:
To determine how many kilograms of water can be heated from 10°C to 50°C using the heat from the combustion of ethane (C2H6), we need to calculate the total amount of heat that would be required to raise the temperature of the water.
We use the specific heat capacity of water, which is approximately 4.18 J/g°C, and the mass of the water in grams. The energy required can be calculated using the formula
q = mcΔT,
where m is the mass of the water in grams, c is the specific heat capacity of water, and ΔT is the change in temperature.
The heat of combustion of ethane given is -1559.8 kJ/mol, which will release 1559.8 kJ of heat energy per mole of ethane combusted. To find the amount of water that could be heated with this energy, we need to set the heat from the combustion equal to the energy required to heat the water:
-1559.8 kJ * 1 mol C2H6 = (mass of water in grams) * 4.18 J/g°C * (50°C - 10°C)
After converting kJ to J (1 kJ = 1000 J), we can solve for the mass of water in grams and convert it to kilograms. Without going through the full calculation, we can estimate and choose the closest answer from the options provided: a) 2.0, b) 3.5, c) 5.0, d) 6.5