Step-by-step explanation:
We have 135 g of ice and we place it inside a beaker with hot water. The final temperature of the mixture is 19.7 °C, so the ice will cool the hot water.
The ice will melt and its temperature will increase from 0°C to 19.7 °C (if we suppose that the initial temperature of ice is 0°C).
First we have to determine the amount of energy that the ice absorbed to melt.
ΔHf = Cf * m
Where ΔHf is the amount of energy that the ice will absorb, Cf is the heat of fusion and m is the mass of ice in this case.
Cf = 334 J/g m = 135 g
ΔHf = Cf * m
ΔHf = 334 J/g * 135 g
ΔHf = 45090 J
Once the ice is melted, that sample of water will increase its temperature from 0 °C to 19.7 °C. Let's find the amount of heat that it is necessary to do that.
Q = m * C * ΔT
Where Q is the amount of heat that the water will absorb, C is the specific heta of water and ΔT is the change in temperature.
Q₁ = m * C * ΔT
Q₁ = 135 g * 4.184 J/(g°C) * (19.7 °C - 0.0 °C)
Q₁ = 11127 J
The total amount of energy that the ice will absorb to go from solid ice at 0°C to liquid water at 19.7 °C is:
Qice = Q₁ + ΔHf
Qice = 11127 J + 45090 J
Qice = 56217 J
The ice is absorbing energy from the hot water that was in the beaker. So the heat that the ice gained is the same amount of heat that the hot water released with opposite sign.
Qice = - Qhw
Qhw = -56217 J
The heat that the hot water gave to the ice can be calculated using this formula.
Qhw = m * C * ΔT
We can replace the values that we already know and solve that equation for m to get the initial volume of water in the beaker.
Qhw = m * C * ΔT
- 56217 J = m * 4.184 J/(g *°C) * (19.7 °C - 67.0 °C)
m = -56217 J /(4.184 J/(g*°C) * (-47.3 °C)
m = 284 g
Since the density of water is 1 g/mL, we can convert the mass of water into volume.
Initial volume = 284 g / (1 g/mL)
Initial volume = 284 mL
Now we know the volume of water that was in the beaker before the ice is added, and we are given the mass of ice. We can find the final volume of water in the baker.
Final volume = initial volume + volume from ice
Final volume = 284 mL + 135 g /(1 g/mL)
Final volume = 419 mL
Answer:
a) The initial volume of water in the beaker was 284 mL.
b) The final volume of water in the beaker is 419 mL.