How much heat energy, in kilojoules, is required to convert 37.0g of ice at −18.0 ∘C to water at 25.0 ∘C ?
0.001
To calculate the heat energy required to convert ice at -18.0°C to water at 25.0°C, we need to consider two steps:
Step 1: Heating the ice to 0°C
Step 2: Melting the ice to water at 0°C
Step 3: Heating the water from 0°C to 25.0°C
Step 1: Heating the ice to 0°C
The specific heat capacity of ice is 2.09 J/g°C.
The temperature change required is 0°C - (-18.0°C) = 18.0°C.
The formula to calculate the heat energy is: q = m * c * ΔT, where q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
Substituting the values, we get q1 = 37.0g * 2.09 J/g°C * 18.0°C = 1415.74 J.
Step 2: Melting the ice to water at 0°C
The heat of fusion for ice is 334 J/g.
The mass of ice is 37.0g.
The formula to calculate the heat energy is: q = m * ΔH, where q is the heat energy, m is the mass, and ΔH is the heat of fusion.
Substituting the values, we get q2 = 37.0g * 334 J/g = 12358 J.
Step 3: Heating the water from 0°C to 25.0°C
The specific heat capacity of water is 4.18 J/g°C.
The temperature change required is 25.0°C - 0°C = 25.0°C.
The formula to calculate the heat energy is: q = m * c * ΔT, where q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.
Substituting the values, we get q3 = 37.0g * 4.18 J/g°C * 25.0°C = 3899.5 J.
Total heat energy required: q_total = q1 + q2 + q3 = 1415.74 J + 12358 J + 3899.5 J = 16713.24 J.
To convert the heat energy to kilojoules, divide by 1000:
q_total = 16713.24 J ÷ 1000 = 16.71324 kJ.
Therefore, approximately 16.7 kilojoules (kJ) of heat energy is required to convert 37.0g of ice at -18.0°C to water at 25.0°C.
To calculate the heat energy required to convert ice at -18.0 °C to water at 25.0 °C, we need to consider two steps: (1) heating the ice to its melting point, and (2) melting the ice into water and heating it from its melting point to 25.0 °C.
Step 1: Heating the ice to its melting point
The heat energy required to raise the temperature of a substance can be calculated using the formula: Q = m * c * ΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, we need to heat the ice from -18.0 °C to its melting point, which is 0 °C.
Assuming the specific heat capacity of ice is 2.09 J/g°C, we can calculate the heat energy required:
Q1 = (m1) * (c1) * (ΔT1) = (37.0 g) * (2.09 J/g°C) * (0 °C - (-18.0 °C))
= 37.0 g * 2.09 J/g°C * 18.0 °C
Now, we need to convert the result to kilojoules (kJ):
Q1 = 37.0 g * 2.09 J/g°C * 18.0 °C * (1 kJ / 1000 J)
= (37.0 g * 2.09 * 18.0) / 1000 kJ
Step 2: Melting the ice and heating the water
The heat energy required to melt ice and heat the resulting water can be calculated using the formula: Q = m * ΔHf + m * c * ΔT, where ΔHf is the heat of fusion, and all other variables have the same meaning as above.
We need to calculate the heat energy required to heat the ice from its melting point (0 °C) to the final temperature (25.0 °C).
The specific heat capacity of water is 4.18 J/g°C, and the heat of fusion of ice is 333.55 J/g.
So, we can calculate the heat energy required as follows:
Q2 = (m2) * (c2) * (ΔT2) + (m2) * (ΔHf)
= (37.0 g) * (4.18 J/g°C) * (25.0 °C - 0 °C) + (37.0 g) * (333.55 J/g)
Now, we need to convert the result to kilojoules (kJ):
Q2 = (37.0 g * 4.18 J/g°C * 25.0 °C + 37.0 g * 333.55 J/g) / 1000 kJ
Finally, we can find the total heat energy required by adding the results from Step 1 and Step 2:
Total Heat Energy = Q1 + Q2
Please substitute the values into the formulas to calculate the final answer.
q1 = heat needed to raise T of ice from -18 C to zero C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial)
q2 = heat needed to melt ice at zero C to liquid H2O at zero C.
q2 = mass ice x heat fusion
q3 = heat needed to raise T liquid H2O from zero C to 25 C.
q3 = mass water x specific heat water x (Tfinal-Tinitial)
Total heat is sum of q1, q2, q3.