Final answer:
To find the energy required to heat 8 mol of water from 25 °C to 87 °C, calculate the mass of water, determine the temperature change, then use these values in the formula q = mcΔT. Using the specific heat capacity of water, we find the energy needed is approximately 37.5 kJ.
Step-by-step explanation:
To calculate the amount of energy needed to heat 8 mol of water from 25 °C to 87 °C, we 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. Given that the specific heat capacity of water is 4.2 J g-1 °C-1 (or 4.184 J/g °C for more precision), we'll use 4.184 J/g °C for this calculation.
First, we need to determine the mass of 8 mol of water. Since the molar mass of water (H2O) is approximately 18 g/mol, the mass of 8 mol is 8 mol × 18 g/mol = 144 g. Next, we calculate the temperature change: ΔT = 87 °C - 25 °C = 62 °C.
Plugging these values into the formula for q, we get:
q = mcΔT = 144 g × 4.184 J/g °C × 62 °C = 37,483.488 J or approximately 37.5 kJ (since 1 kJ = 1,000 J). Therefore, approximately 37.5 kJ of energy is required to heat 8 mol of water from 25 °C to 87 °C.