Question

A chemical reaction takes place inside a flask submerged in a water bath. The water bath contains 6.00 kg of water at 26.9°C. During the reaction, 126 kJ of heat flows out of the flask and into the bath. Calculate the new temperature of the water bath. You can assume the specific heat capacity of water under these conditions is 4.18 J*g⁻¹ * K⁻¹.

Answer 1

To calculate the new temperature of the water bath, the specific heat capacity formula was used. After converting the mass of water to grams and plugging in the given values into the equation, the temperature change was found to be 5.0°C. Adding this to the initial temperature, the final water bath temperature is 31.9°C.

Step-by-step explanation:

The question pertains to calculating the new temperature of a water bath after a chemical reaction has released heat energy into it. Given that the water bath initially contains 6.00 kg of water at 26.9°C and that 126 kJ of heat is added, we can find the final temperature using the specific heat capacity formula:

q = mcΔT where q is heat absorbed, m is mass, c is specific heat capacity, and ΔT is the change in temperature. Since we have the values, we can solve for ΔT and then find the new temperature.

To begin, convert the mass of water from kilograms to grams (6.00 kg = 6000 g) because the specific heat capacity is given in J/g°C. Next, calculate the change in temperature using the formula ΔT = q/(mc). We already have q = 126,000 J (since 1 kJ = 1000 J), m = 6000 g, and c = 4.18 J/g°C. Plugging these into the equation gives:

ΔT = 126,000 J / (6000 g x 4.18 J/g°C) = 5.0°C

Now, add this temperature change to the initial temperature of the water bath to find the final temperature.

New temperature = 26.9°C + 5.0°C = 31.9°C

Therefore, the new temperature of the water bath is 31.9°C.