Determine mass of iron heated to 85.0 degrees C to add to 54.0 g of ice to produce water at 12.5 degrees C. The specific heat of iron is 0.045 J/g C.
[mass Fe x specific heat Fe x (Tf-Ti)] + [mass ice x heat fusion] + [mass H2O from melted ice x specific heat water x (Tf-Ti)] = 0
Tf = final T
Ti = initial T
Solve for mass Fe; that's the only unknown.
To determine the mass of iron needed, we can use the principle of conservation of energy. The heat lost by the iron will be equal to the heat gained by the ice and the water. We can calculate the heat lost by the iron using the formula:
Q = mcΔT
Where:
Q = heat lost or gained (in joules)
m = mass (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the heat gained by the ice and water:
Heat gained by ice:
Q1 = mcΔT1
Where:
m = mass of ice (in grams)
c = specific heat capacity of ice (2.09 J/g°C)
ΔT1 = change in temperature for ice (12.5°C – 0°C)
Next, let's calculate the heat gained by the water:
Heat gained by water:
Q2 = mcΔT2
Where:
m = mass of water (in grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT2 = change in temperature for water (12.5°C – 0°C)
Now, let's calculate the mass of iron needed:
Heat lost by iron = Heat gained by ice + Heat gained by water
mcΔT = mcΔT1 + mcΔT2
m(iron) = (mcΔT1 + mcΔT2) / c(iron)
Substituting the values into the equation:
m(iron) = (m(ice) * c(ice) * ΔT1 + m(water) * c(water) * ΔT2) / c(iron)
m(iron) = (54.0 g * 2.09 J/g°C * 12.5°C + m(water) * 4.18 J/g°C * 12.5°C) / 0.045 J/g°C
Now, we need to know the mass of water to continue with the calculation. If you provide the mass of water, I can help you further calculate the mass of iron needed.