A 27 g ice cube at −25◦C is dropped into a
container of water at 0◦C.
How much water freezes onto the ice? The
specific heat of ice is 0.5 cal/g ·
◦ C and its heat
of fusion of is 80 cal/g.
Answer in units of g.
0.675 g
To determine how much water freezes onto the ice, we need to calculate the amount of heat transferred from the water to the ice.
Step 1: Calculate the heat required to raise the temperature of the ice cube from -25◦C to 0◦C.
Q1 = m1 * c1 * ΔT1
Where:
- m1 is the mass of the ice cube (27 g)
- c1 is the specific heat of ice (0.5 cal/g · ◦C)
- ΔT1 is the change in temperature (0◦C - (-25◦C) = 25◦C)
Q1 = 27 g * 0.5 cal/g ◦C * 25◦C
Q1 = 337.5 cal
Step 2: Calculate the heat required to melt the ice cube.
Q2 = m1 * Lf
Where:
- m1 is the mass of the ice cube (27 g)
- Lf is the heat of fusion of ice (80 cal/g)
Q2 = 27 g * 80 cal/g
Q2 = 2160 cal
Step 3: Calculate the total amount of heat transferred.
Q = Q1 + Q2
Q = 337.5 cal + 2160 cal
Q = 2497.5 cal
Step 4: Calculate the mass of water that freezes onto the ice.
Q = m2 * Lf
Where:
- m2 is the mass of water that freezes onto the ice (unknown)
- Lf is the heat of fusion of ice (80 cal/g)
2497.5 cal = m2 * 80 cal/g
Dividing both sides of the equation by 80 cal/g:
m2 = 2497.5 cal / 80 cal/g
m2 ≈ 31.22 g
Therefore, approximately 31.22 g of water will freeze onto the ice.
To find out how much water freezes onto the ice, we need to calculate the amount of heat transferred from the water to the ice in order to cause the temperature of the ice to reach 0°C and then to change from solid to liquid state.
Here are the steps to find the answer:
Step 1: Calculate the heat required to raise the temperature of the ice from -25°C to 0°C.
- We use the specific heat formula: Q = m * c * ΔT
- Q: Heat energy absorbed/released
- m: Mass of the substance
- c: Specific heat capacity
- ΔT: Change in temperature
Since the ice is being raised from -25°C to 0°C, ΔT = (0 - (-25)) = 25°C
Mass of the ice (m) = 27g
Specific heat of ice (c) = 0.5 cal/g·°C
Therefore, the heat required to raise the temperature of the ice is:
Q1 = m * c * ΔT = 27g * 0.5 cal/g·°C * 25°C = 337.5 cal
Step 2: Calculate the heat required to change the ice into water at 0°C.
- We use the heat of fusion formula: Q = m * ΔHf
- Q: Heat energy absorbed/released
- m: Mass of the substance
- ΔHf: Heat of fusion
Since the ice is changing into water at 0°C, ΔHf = 80 cal/g
Mass of the ice (m) = 27g
Therefore, the heat required to change the ice into water is:
Q2 = m * ΔHf = 27g * 80 cal/g = 2160 cal
Step 3: Add up the heat required in Steps 1 and 2 to find the total heat transferred.
Total heat transferred = Q1 + Q2 = 337.5 cal + 2160 cal = 2497.5 cal
Step 4: Calculate the mass of water that freezes onto the ice.
- The heat that is transferred from the water to the ice is equal to the heat required to freeze the water that freezes onto the ice.
- The heat required to freeze a certain mass (m') of water is given by the heat of fusion formula: Q = m' * ΔHf
Rearranging the formula, we can solve for m':
m' = Q / ΔHf
Substituting the values, we have:
m' = 2497.5 cal / 80 cal/g = 31.2 g
Therefore, approximately 31.2 grams of water will freeze onto the ice.