Answer:
51.84 °C
Step-by-step explanation:
The final temperature of the mixture can be calculated using the formula for the conservation of energy, which states that the total energy of a closed system is constant. To calculate the final temperature, we need to calculate the total energy of the two water samples before they are combined and then calculate the total energy of the mixture.
The heat capacity of water is 4.184 J/g°C, so the heat absorbed or lost by a sample of water can be calculated using the equation:
q = m * c * ΔT
where m is the mass of the water, c is the heat capacity of water, and ΔT is the change in temperature.
For the 420.0 mL of water at 25.00 °C:
m = 420.0 mL * 1.00 g/mL = 420.0 g
c = 4.184 J/g°C
ΔT = 95.00 °C - 25.00 °C = 70.00 °C
q = m * c * ΔT = 420.0 g * 4.184 J/g°C * 70.00 °C = 178584 J
For the 100.0 mL of water at 95.00 °C:
m = 100.0 mL * 1.00 g/mL = 100.0 g
c = 4.184 J/g°C
ΔT = 95.00 °C - 25.00 °C = 70.00 °C
q = m * c * ΔT = 100.0 g * 4.184 J/g°C * 70.00 °C = 296280 J
The total energy of the two water samples before they are combined is:
E = q1 + q2 = 178584 J + 296280 J = 474864 J
After the two water samples are combined, the total mass of the mixture is:
m = 420.0 g + 100.0 g = 520.0 g
The final temperature of the mixture can be calculated using the equation:
Tfinal = E / (m * c) = 474864 J / (520.0 g * 4.184 J/g°C) = 51.84 °C
So the final temperature of the mixture is 51.84 °C.