Final answer:
To find the change in temperature when using 192 ml of water, divide the original temperature change by the factor by which the volume increases. In this case, it's approximately a 3.84-fold increase, leading to a reduced temperature change of around 2.6 °C.
Step-by-step explanation:
The question is about calculating the change in temperature when different volumes of water are used in a reaction. Using the principles of thermochemistry and assuming that the amount of heat produced by the reaction doesn't change with the volume of the solutions, we can infer that increasing the amount of water would result in a smaller temperature change since the same amount of heat would be distributed over a greater mass of water.
As the information suggests, a two-fold increase in the volume of water results in a two-fold decrease in the temperature change. If 50.0 ml of water increased in temperature by 10.0 °C, then using 192 ml of water, which is approximately 3.84 times the original amount (192 ml / 50 ml = 3.84), should reduce the temperature change by roughly the same factor. Therefore, the change in temperature for 192 ml of water can be estimated by dividing the original temperature change, 10.0 °C, by 3.84, which would yield approximately 2.6 °C.