Final answer:
If 42.7 ml of water were used instead of 50.0 ml in a reaction that increased the water's temperature by 10.0 °C, then the temperature of the 42.7 ml of water would be expected to increase by approximately 11.7 °C due to the inverse proportional relationship between volume and temperature change.
Step-by-step explanation:
The question involves understanding how the change in temperature of water is affected by the volume of water used in a reaction at constant pressure.
When considering the same amount of energy being transferred, if the volume of water changes, the temperature change will be inversely proportional to the volume. In the initial scenario, 50.0 ml of water increased in temperature by 10.0 °C.
When the volume of water decreases to 42.7 ml but the same amount of energy is involved, we would expect a larger temperature change because the energy will be distributed over a smaller amount of water.
The specific heat capacity of water indicates that it takes 4.184 joules to raise the temperature of 1 gram of water by 1 °C (or 1 ml of water, since its density is approximately 1 g/ml). Using proportions, we calculate the expected temperature change for 42.7 ml of water.
The calculation is based on the proportional relationship between water volume and temperature change:
- Initial condition: Volume (V1) = 50.0 ml, Temperature change (ΔT1) = 10.0 °C
- Final condition: Volume (V2) = 42.7 ml, Temperature change (ΔT2) = ?
- ΔT2 = ΔT1 x (V1 / V2)
- ΔT2 = 10.0 °C x (50.0 ml / 42.7 ml)
- ΔT2 ≈ 11.7 °C
Therefore, if 42.7 ml of water were used instead of 50.0 ml, the water's temperature would be expected to increase by approximately 11.7 °C.