Question

When a 0.450 g sample of a mixture of volatile hydrocarbons is burned in a bomb calorimeter with a heat capacity of 3440 J/°C, the temperature rises by 7.00 °C.

What is the change in energy (in kilojoules)?
KJ
Calculate the energy change by the combustion of a 5.00 g sample of the same mixture. kJ

Answer 1

The energy change for the 0.450 g sample burned in the bomb calorimeter is 24.080 kJ. When scaling up to a 5.00 g sample, the energy change is 267.556 kJ.

Step-by-step explanation:

To calculate the energy change when a sample of a volatile hydrocarbon mixture is burned in a bomb calorimeter, you multiply the heat capacity of the calorimeter by the temperature change. The heat capacity given is 3440 J/°C, and the temperature rises by 7.00 °C. By multiplying these two values, we find the energy change:

Energy Change = Heat Capacity × Temperature Change = 3440 J/°C × 7.00 °C = 24080 J

To express this in kilojoules (kJ), convert joules to kilojoules (1000 J = 1 kJ):

Energy Change = 24080 J / 1000 = 24.080 kJ

For calculating the energy change for a 5.00 g sample of the same mixture, scale the energy change according to the mass:

Energy Change (5.00 g) = (Energy Change (0.450 g) / 0.450 g) × 5.00 g

Energy Change (5.00 g) = (24.080 kJ / 0.450 g) × 5.00 g = 267.556 kJ

Answer 2

After burning a 0.450 g hydrocarbon sample, 24.080 kJ of energy was released. For a 5.00 g sample, 267.562 kJ of energy would be released. This calculation assumes that the energy released scales linearly with the mass of the sample.

Step-by-step explanation:

To calculate the change in energy when the hydrocarbon mixture is burned, we use the calorie meter's heat capacity and the temperature change. For the first sample of 0.450 g:

• Calorimeter heat capacity = 3440 J/°C
• Temperature rise = 7.00 °C

The energy change (q) is calculated by multiplying the heat capacity by the temperature change:

q = heat capacity × temperature change

q = 3440 J/°C × 7.00 °C = 24080 J

Convert to kilojoules by dividing by 1000:

q = 24.080 kJ

For the 5.00 g sample:

The ratio of the mass of the second sample to the first sample is:

Mass ratio = 5.00 g / 0.450 g

Mass ratio = 11.111 (rounded to three decimal places)

Since the amount of heat released is directly proportional to the mass of the sample burned, we can multiply the energy change by the mass ratio:

Energy change for 5.00 g = 24.080 kJ × 11.111

Energy change for 5.00 g = 267.562 kJ (rounded to three decimal places)