Final answer:
The initial temperature of the quartz sample is 45.6°C.
Step-by-step explanation:
To solve this problem, we need to use the formula Q = mcΔT, where Q is the heat transferred, m is the mass of the quartz sample, c is the specific heat capacity of the quartz sample, and ΔT is the change in temperature. We are given that the initial temperature of the water in the calorimeter is 21°C, and the final temperature is 23.8°C, so we can calculate the change in temperature as follows:
ΔT = Tfinal - Tinitial = 23.8°C - 21°C = 2.8°C
Next, we need to calculate the mass of the quartz sample. We are given that the sample has a mass of 59.4 g, so we can use this value to calculate the heat transferred.
Q = mcΔT = (59.4 g) × (0.730 J/g°C) × (2.8°C) = 167.84 J
Since the pressure remains constant at 1 atm, we can use the formula Q = nRT, where n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. We know that the temperature is in Celsius, so we need to convert it to Kelvin before using the formula.
T = 23.8°C + 273.15 K = 296.95 K
Now we can use the formula to calculate the number of moles of gas:
n = Q / RT = 167.84 J / (8.314 J/mol°K) × (296.95 K) = 0.0205 mol
Finally, we can use the formula Q = mcΔT to calculate the initial temperature of the quartz sample:
Tinitial = Tfinal - ΔT = 296.95 K - 2.8°C = 45.6°C
Therefore, the initial temperature of the quartz sample is 45.6°C.