### Video Transcript

When burned, 40.1 grams of methane,
๐ ๐ equals 16.04 grams per mole, was found to raise the temperature of 10
kilograms of water by 53 degrees Celsius. What is the molar enthalpy change,
to the nearest whole number, for the combustion of methane? Take the specific heat capacity of
water to be 4.2 joules per gram degrees Celsius.

Combustion is an example of an
exothermic reaction, which is a type of reaction that releases energy. In a calorimetry experiment,
methane can be combusted in a bomb calorimeter. As the reaction occurs, there is a
transfer of thermal energy from the reaction system to the surrounding water. This thermal energy heats up the
water, raising its temperature. One assumption we are making is
that all the energy produced during the reaction only heats up the water and no
energy is lost to the surrounding environment.

We can calculate the energy
transferred during the chemical reaction by using the following equation, in which
๐ is the energy transferred in joules. ๐ is the mass in grams. ๐ is the specific heat
capacity. And ฮ๐ก is the change in
temperature in degrees Celsius. The specific heat capacity of a
substance is the quantity of energy in joules required to raise the temperature of
one gram of substance by one degree Celsius.

We are told to take the specific
heat capacity of water to be 4.2 joules per gram degrees Celsius. We also know that the mass of water
is 10 kilograms and the change in temperature of the water is 53 degrees
Celsius.

Itโs important to note that the
units for specific heat capacity include grams, but the mass of water is given in
kilograms. Therefore, letโs convert the mass
of water into grams by multiplying by 1000 grams per kilogram, which gives us 10000
grams.

We can now substitute the values
into our equation to determine the value of ๐ to be 2226000 joules. This is a very large value to work
with, so letโs convert it back into units of kilojoules by dividing by 1000. The value of ๐ is therefore 2226
kilojoules.

Now that we know how much heat was
transferred to the water, we need to calculate the molar enthalpy change, which is
the enthalpy change per mole of methane combusted. We can calculate the number of
moles of methane by dividing the mass of methane by its molar mass. We are told that the mass of
methane is 40.1 grams and the molar mass is 16.04 grams per mole. After dividing, we get the number
of moles of methane. We can now calculate the molar
enthalpy change by dividing the amount of energy transferred during the reaction,
which was 2226 kilojoules, by the number of moles of methane.

Now that weโve calculated the molar
enthalpy change, we need to round our answer to the nearest whole number. After rounding, we get 890
kilojoules per mole. Finally, we need to consider the
sign this value should have. A positive sign is used for
endothermic reactions to indicate that energy is absorbed by the system from the
surroundings. A negative sign is used for
exothermic reactions to indicate energy is released or lost from the system to the
surroundings. A combustion reaction is an
exothermic reaction, and we know heat was released to the water. So we need to use a negative
sign.

Therefore, the molar enthalpy
change for the combustion of methane is a negative 890 kilojoules per mole.