Calculate the enthalpy change for the conversion of 36.04 g of ice at -23.0 °C to water at
75.0 °C under a constant pressure of 1 atm.
The specific heats of ice and water are 2.09 J/(°C . g ) and 4.18 J/(°C . g ) respectively.
The heat of fusion of ice is 6.01 kJ/mol.
how do I solve this??
q1 = heat to raise T of ice at -2 to zero C.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial)
q2 = heat to change ice at zero C to liquid water at zero C.
q2 = mass ice x heat fusion water.
q3 = heat to raise T of water at zero C to water at 75 C.
Then q total = q1 + q2 + q3
To solve this problem, you need to consider the energy changes at different stages of the process:
1. Determine the energy required to raise the temperature of the ice from -23.0 °C to 0 °C.
- Use the equation Q = m * ΔT * C, where Q is the energy change, m is the mass of the ice, ΔT is the temperature change, and C is the specific heat capacity of ice.
- In this case, m = 36.04 g, ΔT = (0 °C - (-23.0 °C)) = 23.0 °C, and C = 2.09 J/(°C . g).
- Calculate Q1 using the given values: Q1 = 36.04 g * 23.0 °C * 2.09 J/(°C . g).
2. Determine the energy required to melt the ice at 0 °C into water at 0 °C.
- The energy required to melt one gram of ice is known as the heat of fusion, which is given as 6.01 kJ/mol.
- However, you need to convert grams to moles of ice before calculating the energy change, using the molar mass of water (18.02 g/mol).
- Calculate the moles of ice: moles = mass of ice / molar mass of ice.
- Calculate Q2 using the given heat of fusion and moles: Q2 = heat of fusion * moles.
3. Determine the energy required to raise the temperature of the water from 0 °C to 75.0 °C.
- Use the same equation as before, Q = m * ΔT * C.
- In this case, the mass of water is the same as the mass of the ice, 36.04 g, ΔT = (75.0 °C - 0 °C) = 75.0 °C, and C is the specific heat capacity of water, which is 4.18 J/(°C . g).
- Calculate Q3 using the given values: Q3 = 36.04 g * 75.0 °C * 4.18 J/(°C . g).
4. Finally, calculate the total enthalpy change by adding up the energy changes at each stage: ∆H = Q1 + Q2 + Q3.
Substitute the given values into the equations and perform the calculations to find the enthalpy change for the conversion of ice to water.