how much heat (in KJ) is evolved in coverting 1.00 mol of steam at 135.0 degrees celcius to ice at -45.0 degrees celcius? the heat capacity of steam is 12.0 J/g * C and ice is 2.09 J/c * C.
35*
You do this in steps. First, note the correct spelling of celsius.
q1 = heat to move steam from 135 C to 100 C.
q1 = mass x heat capacity steam x (Tfinal-Tinitial)=?? where, in this case, Tfinal = 100 and Tinitial = 135.
q2 = heat evolved in condensing vapor at 100 to a liquid.
q2 = mass x heat of vaporization=??
q3 = heat evolved in cooling water from 100 C to 0 C.
q3 = mass x heat capacity of water x (Tf-Ti) = ??
q4 = heat evolved in freezing the ice (from liquid to solid) but leaving the T at 0 C.
q4 = mass x heat of fusion = ??
q5 = heat evolved in moving T of ice from 0 C to -45 C.
q5 = mass x heat capacity ice x (Tfinal-Tinitial) = ??
Now add q1+q2+q3+q4+q5, and change the total from Joules to kJ. Post your work if you get stuck.
To calculate the heat evolved, we need to consider the following steps:
1. Calculate the heat to cool steam to 0°C.
2. Calculate the heat to freeze water at 0°C to ice at 0°C.
3. Calculate the heat to cool ice from 0°C to -45°C.
Let's calculate the heat for each step:
Step 1: Calculating the heat to cool steam to 0°C.
The molar mass of water is approximately 18.015 g/mol.
The specific heat capacity of steam is 12.0 J/g°C.
First, we need to calculate the heat to decrease the temperature of 1 mol of steam from 135.0°C to 0°C:
Heat 1 = (Temperature change) x (Molar mass) x (Specific heat capacity)
Heat 1 = (0°C - 135.0°C) x (18.015 g/mol) x (12.0 J/g°C)
Step 2: Calculating the heat to freeze water to ice at 0°C.
The heat of fusion for water is approximately 333.55 J/g.
We need to calculate the heat to freeze 1 mol of water at 0°C to ice at 0°C:
Heat 2 = (Molar mass) x (Heat of fusion)
Heat 2 = (18.015 g/mol) x (333.55 J/g)
Step 3: Calculating the heat to cool ice from 0°C to -45°C.
The specific heat capacity of ice is 2.09 J/g°C.
We need to calculate the heat to decrease the temperature of 1 mol of ice from 0°C to -45°C:
Heat 3 = (Temperature change) x (Molar mass) x (Specific heat capacity)
Heat 3 = (-45°C - 0°C) x (18.015 g/mol) x (2.09 J/g°C)
Now let's add up all the heats to get the total heat evolved:
Total Heat = Heat 1 + Heat 2 + Heat 3
Remember to convert the units to kilojoules (kJ) by dividing by 1000.
I'll calculate it step-by-step:
Heat 1 = (0°C - 135.0°C) x (18.015 g/mol) x (12.0 J/g°C) = -29112.32475 J
Heat 2 = (18.015 g/mol) x (333.55 J/g) = 5972.36025 J
Heat 3 = (-45°C - 0°C) x (18.015 g/mol) x (2.09 J/g°C) = -1704.80825 J
Total Heat = (-29112.32475 J) + (5972.36025 J) + (-1704.80825 J)
Total Heat = -21248.77275 J
Converting to kilojoules (kJ):
Total Heat = -21248.77275 J / 1000 = -21.248 kJ
Therefore, approximately -21.248 kJ of heat is evolved in converting 1.00 mol of steam at 135.0°C to ice at -45.0°C. The negative sign indicates an exothermic process.
To calculate the heat evolved in converting steam to ice, you need to consider two steps: heating the steam to its boiling point and then cooling it to the final temperature of ice.
Step 1: Calculate the heat required to heat the steam from 135.0°C to its boiling point at 100.0°C.
The heat capacity of steam is given as 12.0 J/g * °C.
First, find the temperature change by subtracting the initial temperature from the boiling point: 100.0°C - 135.0°C = -35.0°C.
Next, calculate the heat required using the formula: q = n * C * ΔT
Where: q is the heat absorbed, n is the number of moles, C is the heat capacity, and ΔT is the temperature change.
Convert the number of moles to grams using the molar mass of steam: 1.00 mol * 18.02 g/mol = 18.02 g.
Now, substitute the values into the formula: q = 18.02 g * 12.0 J/g°C * (-35.0°C).
Calculate q: q = -7566 J.
Divide by 1000 to convert the answer to kilojoules: q = -7.566 kJ.
Step 2: Calculate the heat released when cooling the steam from its boiling point to -45.0°C.
The heat capacity of ice is given as 2.09 J/g°C.
Again, find the temperature change: -45.0°C - 0.0°C = -45.0°C.
Substitute the values into the heat formula: q = n * C * ΔT.
q = 18.02 g * 2.09 J/g°C * (-45.0°C).
Calculate q: q = -1702 J.
Divide by 1000 to convert to kilojoules: q = -1.702 kJ.
The total heat evolved in converting 1.00 mol of steam at 135.0°C to ice at -45.0°C is the sum of the heat values from steps 1 and 2:
Total heat = (-7.566 kJ) + (-1.702 kJ) = -9.268 kJ.
Therefore, approximately 9.268 kJ of heat is evolved in converting 1.00 mol of steam at 135.0°C to ice at -45.0°C.