Final answer:
To find the required heat energy to raise the temperature of 163.0 g of water from 25.0°C to 75.0°C, we use the specific heat capacity of water and the mass and temperature change to calculate 8.15 kcal, with 9.5 kcal being the closest provided option.
Step-by-step explanation:
To calculate the amount of heat energy required to raise the temperature of water, we can use the formula q = mcΔT, where q is the heat energy in joules, m is the mass in grams, c is the specific heat capacity, and ΔT is the change in temperature in degrees Celsius. The specific heat capacity of water is 4.184 J/g°C. Thus, for 163.0 g of water, the temperature change ΔT is 75.0°C - 25.0°C, which equals 50.0°C. Using the formula:
q = (163.0 g)(4.184 J/g°C)(50.0°C)
We get q = 34098 J, which we can convert to kilocalories knowing that 1 kcal = 4184 J. Therefore:
q = 34098 J ÷ 4184 J/kcal ≈ 8.15 kcal
However, since this option isn't available in the choices provided by the student, it's likely that a rounding error has occurred either in the student's options or in the calculation presented. Among the options given by the student, Option 1: 9.5 kcal is the closest to our calculated value.