Question Video: Calculating the Mass of Fuel Needed to Boil Water Chemistry

A student wants to take 150 mL of water at 25°C and boil it. They are given some fuel that produces 6.75 kJ of heat energy per 1 g of fuel burned. How much fuel does the student need to burn in order for the water to reach its boiling point? Give your answer to the nearest whole number. Assume the heat capacity of water remains constant.

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Video Transcript

A student wants to take 150 milliliters of water at 25 degrees Celsius and boil it. They are given some fuel that produces 6.75 kilojoules of heat energy per one gram of fuel burned. How much fuel does the student need to burn in order for the water to reach its boiling point? Give your answer to the nearest whole number. Assume the heat capacity of water remains constant.

There’s a lot of information in this question, so let’s break it down. A student has 150 milliliters of water at 25 degrees Celsius. They want to boil the water. Water boils at 100 degrees Celsius. So the student will need to increase the temperature of the water by 75 degrees. To do this, the student is given a fuel to burn. We are told that 6.75 kilojoules of heat energy is produced per one gram of fuel burned. We need to assume for this question that all of the heat energy produced by the fuel is transferred to the water when in reality some of this energy would be transferred to the surroundings. Using all of this information, we need to determine how much fuel needs to be burned in order for the water to boil.

To answer the question, we’ll first need to determine the amount of energy needed to boil the water. For this, we’ll need to use the equation 𝑞 equals 𝑚𝑐Δ𝑡. In this equation, 𝑞 is the energy in joules, 𝑚 is the mass in grams, 𝑐 is the specific heat capacity in joules per gram per degree Celsius. The specific heat capacity, as the unit suggests, is the amount of energy in joules required to raise the temperature of one gram of a substance by one degree Celsius. Finally, Δ𝑡 represents the change in temperature in degrees Celsius.

To determine 𝑞, the amount of energy needed to boil the water, we need to identify 𝑚, 𝑐, and Δ𝑡. We were given the volume of water, not the mass. But we can make use of the fact that one milliliter of water has a mass of one gram. So 150 milliliters of water has a mass of 150 grams.

Next, we need to recall that the specific heat capacity of water is 4.184 joules per gram per degrees Celsius. This value does change slightly as the temperature of water increases. But we are told in the question to assume it is constant.

Finally, we know that the temperature of the water needs to increase from 25 degrees Celsius to 100 degrees Celsius. This means that the change in temperature is 75 degrees Celsius. We can then plug the values for 𝑚, 𝑐, and Δ𝑡 into the equation. The gram and degrees Celsius units will cancel, leaving us with the unit joules. Performing the calculation gives us an answer of 47070 joules.

We could also report this value in kilojoules by recognizing that 1000 joules is equal to one kilojoule. We can convert from joules to kilojoules by multiplying by one kilojoule per 1000 joules. The joule units will cancel, and we’ll get a value of 47.07 kilojoules.

Now that we know the amount of energy needed to boil the water, we can determine the mass of fuel needed to supply this amount of energy. We know that each gram of fuel burned will release 6.75 kilojoules of heat energy. So, to calculate the mass, we can divide the amount of energy required by the amount of energy released per gram of fuel. The kilojoule units will cancel, leaving us with the unit grams. Performing the calculation gives us an answer of 6.973 grams.

The question asks us to give our answer to the nearest whole number. So, to the nearest whole number, the amount of fuel the student needs to burn in order for the water to reach its boiling point is seven grams.