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.)
I am not sure what to do
Heat obtained from CH4 = 891 kJ x 143/16 = ? kJ.
?kJ = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Solve for mass H2O and convert to kg.
molar mass is 16 for CH4
and answer is 23.8 kg
To solve this problem, we need to calculate the amount of heat produced by burning 143 grams of methane and then use that heat to calculate the mass of water heated.
First, let's calculate the amount of heat produced by burning 143 grams of methane. We can do this by using the heat of combustion of methane.
1. Calculate the number of moles of methane:
Molar mass of CH4 = 12.01 g/mol (C) + 4(1.01 g/mol) (4H) = 16.04 g/mol
Number of moles of CH4 = mass of CH4 / molar mass of CH4
Number of moles of CH4 = 143 g / 16.04 g/mol
2. Calculate the heat produced by burning the methane:
Heat produced by burning CH4 = number of moles of CH4 * heat of combustion of CH4
The heat of combustion of CH4 is given as 891 kJ/mol, but we need to convert it to joules:
1 kJ = 1000 J
Heat produced by burning CH4 = (number of moles of CH4) * (heat of combustion of CH4) * 1000 J/kJ
Now that we have the amount of heat produced, we can use it to calculate the mass of water heated. We'll use the specific heat formula:
q = m * c * ΔT
where:
q = amount of heat (in joules)
m = mass of water (in grams)
c = specific heat of water (4.184 J/goC)
ΔT = change in temperature
Rearranging the formula, we can solve for the mass of water:
m = q / (c * ΔT)
Let's substitute the values into the formula:
m = (heat produced by burning CH4) / (specific heat of water * change in temperature)
Substitute the values into the formula and calculate the mass of water.