Question

A biology experiment requires the preparation of a water bath at $37.0°C$(body temperature). The temperature of the cold tap water is $22.0°C$, and the temperature of the hot tap water is $55.0°C$. If a student starts with 90.0 g of cold water, what mass of hot water must be added to reach $37.0°C$?

Short answer

75 grams of hot water must be added to reach $37.0°C$.

Step-by-step solution

Endothermic Reaction

If two reactants at the different temperatures are mixed and the resulting solution gets cooler, it means the reaction is endothermic.

In the question we are adding cool water to hot water so the reaction is also endothermic.

Calculation

$m_{1}C∆T_1=m_{2}C∆T_2$

C is same on both sides, it will cancel out.

$m_1∆T_1=m_2∆T_2$

Where,

$m_1$= mass of cold water = 90.0 g

C = specific heat capacity of water

$m_2$= mass of hot water

$∆T_1=changeintemperatureofcoldwater=37-22°C=15°C$

$\Delta T_2=changeintemperatureofhotwater=55-37°C=18°C$

$$\begin{gathered} 90.0\times 15=m_2\times 18 \\ {m}_2=\frac{90.0\times 15}{18}=75g \end{gathered}$$