How much heat is needed to melt a sample of ice if the temperature of 150 g of water in the calorimeter is lowered from 23.0 C to 0 C?
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To find out how much heat is needed to melt the sample of ice, we need to consider the energy required to lower the temperature of the water from 23.0°C to 0°C and the energy required to melt the ice at 0°C.
First, let's calculate the energy required to lower the temperature of water using the specific heat capacity formula:
Q1 = m * c * ΔT
Where:
Q1 is the energy required (in Joules),
m is the mass of water (in grams),
c is the specific heat capacity of water (4.18 J/g°C), and
ΔT is the change in temperature (in °C).
Given that the mass of water is 150 g, the specific heat capacity of water is 4.18 J/g°C, and the change in temperature is from 23.0°C to 0°C, we can calculate Q1:
Q1 = 150 g * 4.18 J/g°C * (0°C - 23.0°C)
Q1 = -11190 J
The negative sign indicates that the water is losing energy as its temperature decreases.
Next, let's calculate the energy required to melt the ice. The amount of energy required to melt a substance is given by:
Q2 = m * ΔHf
Where:
Q2 is the energy required (in Joules),
m is the mass of ice (in grams), and
ΔHf is the heat of fusion of ice (334 J/g).
Assuming all the water in the calorimeter turns into ice, the mass of ice would be equal to the mass of water:
m = 150 g
Therefore, we can calculate Q2:
Q2 = 150 g * 334 J/g
Q2 = 50100 J
Now, to find the total heat needed to melt the ice, we add Q1 and Q2:
Total heat = Q1 + Q2
Total heat = -11190 J + 50100 J
Total heat = 38910 J
So, approximately 38910 Joules (J) of heat is needed to melt the sample of ice.