A 3.9-g sample of Colorado oil shale is burned in a bomb calorimeter, which causes the temperature of the calorimeter to increase by 5.0°C. The calorimeter contains 1.00 kg of water (heat capacity of H2O = 4.184 J/g°and the heat capacity of the empty calorimeter is 0.10 kJ/°C. How much heat is released per gram of oil shale when it is burned?

To solve this problem, we need to calculate the total heat absorbed by the calorimeter and the water, and then divide it by the mass of the oil shale to find the heat released per gram.

Step 1: Calculate the heat absorbed by the water. The heat absorbed by the water (q_water) can be calculated using the formula q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

q_water = (1000 g)(4.184 J/g°C)(5.0°C) = 20920 J

Step 2: Calculate the heat absorbed by the calorimeter. The heat absorbed by the calorimeter (q_calorimeter) can be calculated using the formula q = CΔT, where C is the heat capacity of the calorimeter and ΔT is the change in temperature.

q_calorimeter = (0.10 kJ/°C)(5.0°C) = 0.5 kJ = 500 J (since 1 kJ = 1000 J)

Step 3: Calculate the total heat absorbed. The total heat absorbed (q_total) is the sum of the heat absorbed by the water and the calorimeter.

q_total = q_water + q_calorimeter = 20920 J + 500 J = 21420 J

Step 4: Calculate the heat released per gram of oil shale. The heat released per gram of oil shale (q_shale) can be calculated by dividing the total heat absorbed by the mass of the oil shale.

q_shale = q_total / mass_shale = 21420 J / 3.9 g = 5492.31 J/g

So, the heat released per gram of oil shale when it is burned is approximately 5492.31 J/g.