Question

2.50 g ch₄ reacts with excess o₂ in a bomb calorimeter containing 400.0 g of water. the temperature increased by 53.5 °c. what amount of heat is absorbed by the water, in kilojoules? c_cal = 925 j/°c c_h₂o = 4.18 j/g° c q_h₂o = ? kj enter the magnitude only.

Explanation:

Step1: Recall the formula for heat absorbed by water

The formula for heat (\(q\)) absorbed by a substance is \(q = mc\Delta T\), where \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature. For water, \(m = 400.0\space g\), \(c = 4.18\space J/g^\circ C\), and \(\Delta T = 53.5^\circ C\).

Step2: Plug in the values into the formula

Substitute the values into the formula: \(q_{H_2O}=m\times c_{H_2O}\times\Delta T\)
\(q_{H_2O}=400.0\space g\times4.18\space J/g^\circ C\times53.5^\circ C\)
First, calculate \(400.0\times4.18 = 1672\)
Then, calculate \(1672\times53.5 = 1672\times50+1672\times3.5 = 83600 + 5852 = 89452\space J\)

Step3: Convert joules to kilojoules

Since \(1\space kJ = 1000\space J\), divide the heat in joules by 1000: \(q_{H_2O}=\frac{89452\space J}{1000}=89.452\space kJ\)

Answer:

89.452