We have of ice at -11.9°C and it is ultimately completely converted to liquid at 9.9°C. For ice, use a specific heat (Cs) of 2.01 J/gK, for liquid water use a specific heat of 4.18 J/gK, and ΔHfusion = 6.01kJ/mole, Molar mass H20 = 18.01g/mol. If 4.19x10^3 kJ is transferred as heat to the ice for the above process is, how many grams of ice are melted and warmed to 9.9°C?
Do this steps.
q1 = energy to raise T from zero for liquid H2O to 9.9 liquid water.
q1 = (mass H2O x specific heat H2o x (Tfinal-Tinitial). You have all of these numbers but mass H2O.
q2 = heat to convert solid ice to liquid water at zero C is
q2 = mass ice x heat fusion. You have heat fusion.
q3 is heat to raise T of solid ice from -11.9 C to solid ice at zero C.
q3 = mass ice x specific heat ice x (Tfinal-Tinitial). You have all but mass ice.
All of these must add up to heat you have and that is 4.19E3 kJ which I would convert to J.
4.19E6J = q1 + q2 + q3. Substitute the equations above for q1, q2, and q3 and solve for mass ice. I estimated about 10,000 grams ice.
To solve this problem, we'll need to consider the following steps:
1. Calculate the amount of heat required to raise the temperature of the ice from -11.9°C to 0°C.
2. Calculate the heat required to completely melt the ice at 0°C.
3. Calculate the amount of heat required to raise the temperature of the melted ice from 0°C to 9.9°C.
4. Add up the heats obtained in steps 1, 2, and 3 to determine the total heat transferred.
5. Divide the total heat transferred by the heat of fusion to find the number of moles of ice melted.
6. Multiply the number of moles of ice by the molar mass of water to obtain the mass of ice melted.
Let's begin:
Step 1: Calculating the heat to raise the temperature of ice from -11.9°C to 0°C.
We'll use the equation: q = m * Cs * ΔT, where q is the heat, m is the mass, Cs is the specific heat, and ΔT is the change in temperature.
The mass of the ice is not given, so we'll assign it the variable "m". We'll assume it later cancels out.
The change in temperature is given by ΔT = 0°C - (-11.9°C) = 11.9°C.
Plugging in the values, we get:
q1 = m * 2.01 J/gK * 11.9°C
Step 2: Calculating the heat required to melt the ice.
The heat of fusion (ΔHfusion) is given as 6.01 kJ/mol. To convert it to J/g, we need to divide by the molar mass of water (18.01 g/mol):
ΔHfusion_g = (6.01 kJ/mol) / (18.01 g/mol)
Since we don't know the number of moles, we'll assign it the variable "n". We'll assume it later cancels out.
The heat required to melt the ice is given by:
q2 = n * ΔHfusion_g
Step 3: Calculating the heat to raise the temperature of the melted ice from 0°C to 9.9°C.
Once again, we'll use the equation: q = m * Cs * ΔT.
The mass of the melted ice is the same as the mass of the ice melted.
The change in temperature is given by ΔT = 9.9°C - 0°C = 9.9°C.
Plugging in the values, we get:
q3 = m * 4.18 J/gK * 9.9°C
Step 4: Calculating the total heat transferred.
The total heat transferred is given by:
q_total = q1 + q2 + q3
Step 5: Calculating the number of moles of ice melted.
We can rearrange the equation for q2 to find the number of moles (n):
n = q2 / ΔHfusion_g
Step 6: Calculating the mass of ice melted.
Finally, we can multiply the number of moles of ice (n) by the molar mass of water to find the mass of ice melted:
mass_melted = n * molar mass H2O
By following these steps, you should be able to determine the number of grams of ice that are melted and warmed to 9.9°C.