Question

Consider a solution prepared by dissolving \(10.00 \mathrm{~g}\) of \(\mathrm{NaOH}\) in \(1.00 \mathrm{~L}\) of water. (a) When the solid dissolves, will the temperature of the solution increase? (b) What is the sign of \(H\) for the process? (c) Will dissolving \(5.00 \mathrm{~g}\) of \(\mathrm{NaOH}\) increase \(\Delta t ?\) (d) Will dissolving one mole of \(\mathrm{NaOH}\) in \(1.00 \mathrm{~L}\) of water increase \(t_{\mathrm{f}} ?\)

Short answer

Answer: Dissolving NaOH in water increases the temperature due to its exothermic nature, releasing heat in the process with a negative enthalpy change (ΔH). When dissolving smaller amounts of NaOH, such as 5.00 g, the change in temperature (Δt) is still positive but smaller compared to dissolving larger amounts, like 10.00 g or one mole (40 g) of NaOH. The final temperature (tf) increases when dissolving one mole of NaOH in 1.00 L of water.

Step-by-step solution

a) Temperature Increase

When NaOH dissolves in water, it releases heat in the process, which is known as an exothermic reaction. Therefore, the temperature of the solution will increase.

b) Sign of Enthalpy Change (H)

Since the process of dissolving NaOH in water is exothermic, the heat is released, which means the enthalpy change (ΔH) for the process is negative, as the system loses heat to the surroundings. Hence, the sign of H for the process is negative: ΔH < 0.

c) Dissolving 5 g of NaOH and Δt

Since dissolving NaOH in water is an exothermic process, dissolving a smaller amount of NaOH, such as 5.00 g, will still result in an increase in temperature but to a lesser extent compared to dissolving 10.00 g of NaOH because less heat (energy) is being released when a smaller amount of NaOH is dissolved in water.

d) Dissolving one mole of NaOH and tf

One mole of NaOH has a mass of approximately 40 g (as per the periodic table). When dissolving NaOH in water, more heat will be released as more NaOH is dissolved. Since dissolving one mole of NaOH (40 g) in 1.00 L of water is more than dissolving 10.00 g or even 5.00 g, the final temperature (tf) of the solution will be higher. Thus, dissolving one mole of NaOH in 1.00 L of water will increase the final temperature (tf).