Chapter U5, Problem 11STP

Interpretation Introduction

Interpretation:

The energy released per gram from the combustion of a fixed mass of potato chips needs to be determined. The energy produced by the combustion reaction is used to heat up a fixed mass of water.

Concept introduction:

As per the principle of thermochemistry, the heat lost by a hot substance is equal to the heat gained by a cold substance when these two substances are brought in contact with each other. The amount of heat energy lost or gained by the substance depends on the mass of the substance taken as well as the rise in temperature of the substance.

In this problem, the combustion of the chips produces energy that is used to heat up the given mass of water. The heat gained by the fixed mass of water is given by the following formula:

$q=mc\Delta T$

Here, q is heat gained, m is mass of water, c is specific heat capacity of water and $\Delta T$ is change in temperature of water.

The specific heat capacity of a substance is constant and is equal to the amount of heat required to raise the temperature of unit mass of the substance by unit degree.

Answer to Problem 11STP

The correct answer is the second option, option (B).

Explanation of Solution

Reason for correct option:

The heat released by the combustion of the chips is used to heat up 25.0 mL of water.

Assuming that the density of water is 1.00 g/mL at the temperature of the experiment, the mass of water heated up can be calculated as

$\begin{array}{c}\text{Mass of water = }\left(\text{volume of water}\right)\times \left(\text{density of water}\right)\\ =\left(25.0\text{ mL}\right)\times \left(1.00\text{ g/mL}\right)\\ =\text{25}\text{.0 g}\end{array}$

$\begin{array}{c}\text{Heat gained by water =}\left(\text{mass of water}\right)\times \\ \left(\text{specific heat capacity of water}\right)\times \\ \left(\text{change in temperature of water}\right)\\ =\left(25.0\text{ g}\right)\times \left(1.00\text{ cal/g}\text{.}°\text{C}\right)\times \left(6.00°\text{C}\right)\\ =150.\text{ cal}\end{array}$

(specific heat capacity of water is 1.00 cal/g.°C)

The heat gained by water must have been obtained from the combustion of the chips; thus, the heat released by the combustion of the chips is 150. cal.

$\begin{array}{c}\text{Heat released by the combustion of the chips =}\left(\text{mass of the chips}\right)\\ \times \left(\text{energy per gram of chips}\right)\end{array}$

Therefore,

$\begin{array}{c}\left(\text{13}\text{.0 g}\right)\times \left(\text{energy per gram of chips}\right)=\text{150}\text{. cal}\\ \Rightarrow \text{energy per gram of chips =}\frac{\left(\text{150}\text{. cal}\right)}{\left(13.0\text{ g}\right)}\\ \Rightarrow \text{energy per gram of chips =11}\text{.53 cal/g}\approx 11.5\text{ cal/g}\end{array}$

Conclusion

Reason for incorrect options:

The mathematical calculation leads to the correct answer as option (B) and thus, all the other options are incorrect.