Questions: A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 6.30 kg of water at 35.1°C. During the reaction 10 kJ of heat flows out of the flask and into the bath. Calculate the new temperature of the bath. Assume the specific heat capacity of water is 4.185 J/g · °C.

Solution Steps

We are given:

• Mass of water, \( m = 6.30 \, \text{kg} \)
• Initial temperature of water, \( T_i = 35.1^\circ \text{C} \)
• Heat added to the water, \( Q = 10 \, \text{kJ} = 10,000 \, \text{J} \)
• Specific heat capacity of water, \( c = 4.185 \, \text{J/g}^\circ \text{C} \)

Since the specific heat capacity is given in \(\text{J/g}^\circ \text{C}\), we need to convert the mass from kilograms to grams: \[ m = 6.30 \, \text{kg} \times 1000 \, \text{g/kg} = 6300 \, \text{g} \]

The formula for heat transfer is: \[ Q = mc\Delta T \] where \(\Delta T\) is the change in temperature. We need to solve for \(\Delta T\): \[ \Delta T = \frac{Q}{mc} \]

Substitute the given values into the formula: \[ \Delta T = \frac{10,000 \, \text{J}}{6300 \, \text{g} \times 4.185 \, \text{J/g}^\circ \text{C}} \] \[ \Delta T = \frac{10,000}{26365.5} \] \[ \Delta T = 0.3793^\circ \text{C} \]

Since the heat flows into the water, the temperature will increase: \[ T_f = T_i + \Delta T \] \[ T_f = 35.1^\circ \text{C} + 0.3793^\circ \text{C} \] \[ T_f = 35.4793^\circ \text{C} \]

Final Answer