Question

You are planning a lecture demonstration to illustrate an endothermic process. You desire to lower the temperature of 1400 mL water in an insulated container from 25 to 10 °C. Approximately what mass of NH₄CI (s) should you dissolve in water to achieve this result? The heat of solution of NH₄CI is +14.7 klJ per mole of NH₄CI. Assume the density of water = 1 g/mL and the heat capacity of the calorimeter is 4.184 J g⁻¹ °C, Show all calculations.

Answer 1

To calculate the mass of NH₄Cl needed to lower the temperature of 1400 mL of water from 25 °C to 10 °C, use the formula q = mcΔT with water's specific heat capacity, and then divide the heat needed by the heat of solution of NH₄Cl to get the mass of NH₄Cl needed.

Step-by-step explanation:

To calculate the mass of NH₄Cl required to lower the temperature of 1400 mL of water from 25 °C to 10 °C in an endothermic process, we need to use the heat of solution and the specific heat capacity of water. First, we find the amount of heat needed to cause the desired temperature change in water using the formula q = mcΔT, where m is mass, c is the specific heat capacity, and ΔT is the change in temperature. The mass of the water (m) is equal to its volume assuming a density of 1 g/mL, which is 1400 g for 1400 mL. The specific heat capacity (c) of water is given as 4.184 J g⁻¹ °C⁻¹. The temperature change (ΔT) is 10 °C - 25 °C = -15 °C. The negative sign indicates that heat is being removed from the water (endothermic process).

Next, we plug the values into q = mcΔT to get q = (1400 g)(4.184 J g⁻¹ °C⁻¹)(-15 °C) to find the heat in joules. Once we have q, we can use the heat of solution of NH₄Cl, which is +14.7 kJ/mol, to find the number of moles necessary to absorb that heat. We convert q from joules to kilojoules by dividing by 1000, and then divide by the heat of solution to get the moles of NH₄Cl required. Finally, we multiply the moles by the molar mass of NH₄Cl (53.49 g/mol) to find the mass needed for the demonstration.