A kettle contains 2kg of water at 20 degree celsius. What mass of methane must be burned to raise this quantity of water to 100 degree celsius?

Look up (or calculate) the heat of combustion for methane. I'll call that Z.

Then Z = mass H2O x specific heat H2O x (Tfinal-Tinitial)
Keep mass and specific heat units consistent.

To find the mass of methane needed to raise the temperature of the water from 20 degree Celsius to 100 degree Celsius, we can use the following steps:

Step 1: Determine the temperature change of the water
The temperature change of the water is calculated by subtracting the initial temperature from the final temperature:
Temperature change = Final temperature – Initial temperature = 100°C - 20°C = 80°C

Step 2: Determine the heat energy required to raise the temperature of the water
The heat energy required to raise the temperature of the water can be calculated using the formula:
Q = mcΔT
where Q is the heat energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the temperature change.

The specific heat capacity of water is approximately 4.18 J/g°C. However, since the given mass of water is in kilograms, we need to convert it to grams.

Step 3: Convert the mass of water from kilograms to grams
Given: Mass of water = 2 kg
To convert kilograms to grams, multiply by 1000:
Mass of water in grams = 2 kg * 1000 g/kg = 2000 g

Step 4: Calculate the heat energy required
Substituting the values into the formula:
Q = 2000 g * 4.18 J/g°C * 80°C = 667,200 J

Step 5: Convert the energy from joules to kilojoules (kJ)
Given: 1 kJ = 1000 J
So, divide the value of Q in joules by 1000:
Energy in kJ = 667,200 J / 1000 = 667.2 kJ

Step 6: Determine the energy released per mole of methane burned
To calculate the energy released per mole of methane burned, we need to know the enthalpy change of combustion of methane. The enthalpy change of combustion of methane is approximately -890 kJ/mol. This means that for every mole of methane burned, 890 kJ of energy is released.

Step 7: Calculate the moles of methane needed
Divide the energy required (667.2 kJ) by the energy released per mole of methane (-890 kJ/mol):
Moles of methane = Energy required / Energy released per mole of methane = 667.2 kJ / -890 kJ/mol

Note: In this calculation, the negative sign is used to indicate the energy released.

Step 8: Calculate the mass of methane needed
Finally, to calculate the mass of methane, we need to know its molar mass. The molar mass of methane (CH₄) is approximately 16 g/mol.

Using the formula:
Mass of methane = Moles of methane * Molar mass of methane

Plug in the value of moles of methane and the molar mass:
Mass of methane = Moles of methane * Molar mass of methane = Moles of methane * 16 g/mol