Determine the amount of heat needed to raise 20.0 g of ice at 0 degrees C to steam at 100 degrees C. (ΔHfusion = 334 J/g; Specific heat of (H2O) = 4.18 J/gc; ΔHvap = 2.25 kJ/g)
q1 = heat to melt ice.
q1 = mass ice x heat fusion.
q2 = heat need to raise temperature for liquid water from zero C to liquid water at 100 C.
q2 = mass melted ice x specific heat water x (Tfinal-Tinitial)
q3 = heat needed to vaporize the steam at 100 C.
q3 = mass water x heat vaporization.
Total Q = q1 + q2 + q3.
i am getting 60040J. Is that correct?
60.040 kJ is correct.
Ok I see. thank you very much :-)
To determine the amount of heat needed to raise the ice to steam, we need to consider the different stages of the process and the corresponding heat changes.
First, we need to calculate the heat required to warm the ice from 0°C to its melting point. This is done using the formula:
Q = m * ΔHfusion
where:
Q is the heat required (in joules)
m is the mass of ice (in grams)
ΔHfusion is the heat of fusion (334 J/g)
Substituting the values, we have:
Q = 20.0 g * 334 J/g = 6,680 J
Next, we need to consider the heat required to melt the ice into water at 0°C. This is calculated using the formula:
Q = m * ΔHfusion
In this case, the mass remains the same (20.0 g), but the heat of fusion needs to be converted to joules. ΔHfusion is given in joules per gram, so we need to convert it to kilojoules per gram by dividing by 1000:
ΔHfusion = 334 J/g = 0.334 kJ/g
Now substituting the values, we have:
Q = 20.0 g * 0.334 kJ/g = 6.68 kJ
Moving on, once all the ice has melted, we need to consider the heat required to raise the temperature of the water from 0°C to 100°C. This is calculated using the formula:
Q = m * c * ΔT
where:
Q is the heat required (in joules)
m is the mass of water (in grams)
c is the specific heat of water (4.18 J/g°C)
ΔT is the change in temperature (100°C - 0°C = 100°C)
Substituting the values, we have:
Q = 20.0 g * 4.18 J/g°C * 100°C = 8,360 J
Finally, we need to consider the heat required to vaporize the water at 100°C into steam. This is calculated using the formula:
Q = m * ΔHvap
where:
Q is the heat required (in joules)
m is the mass of water (in grams)
ΔHvap is the heat of vaporization (2.25 kJ/g)
Substituting the values, we have:
Q = 20.0 g * 2.25 kJ/g = 45 kJ
To find the total heat required, we sum up the heat changes from each stage:
Total heat required = Heat to melt ice + Heat to warm water + Heat to vaporize water
Total heat required = 6.68 kJ + 8,360 J + 45 kJ
Converting all the units to kilojoules:
Total heat required = 6.68 kJ + 8.36 kJ + 45 kJ = 60.04 kJ
Therefore, the amount of heat needed to raise 20.0 g of ice at 0°C to steam at 100°C is 60.04 kJ.