Determine the mass of iron heated to 85 Celsius to add to 54.0g of ice to produce water at 12.5 Celsius. The speciic heat of iron is 0.045J/g C
What steps do I take to solve this problem? Thanks
heatgainedbyiron+heatgained by water+heatgainedmelting ice=0
Some of these will be negative (heat lost)
massiron*ciron*(12.5-85)+54*cwater*(12.5-0)+54*hfusionice=0
solve for mass of iron.
the answer by bobpursley is incorrect.
the correct answer is 6377.4g
To solve this problem, you can follow these steps:
1. Determine the heat required to heat the iron from its initial temperature to the final temperature:
- Determine the thermal energy using the formula: Q = m * c * ∆T
- Where Q is the heat energy, m is the mass of iron, c is the specific heat of iron, and ∆T is the change in temperature.
- Plug in the given values: Q = m * 0.045 J/g°C * (12.5°C - 85°C)
2. Determine the heat required to melt the ice and raise its temperature from 0°C to the final temperature:
- Determine the heat required to melt the ice using the formula: Q = m * ΔHf
- Where Q is the heat energy, m is the mass of ice, and ΔHf is the heat of fusion for ice (which is 334 J/g).
- Determine the heat required to heat the melted ice using the formula: Q = m * c * ∆T
- Where Q is the heat energy, m is the mass of water, c is the specific heat of water (which is approximately 4.18 J/g°C), and ∆T is the change in temperature.
- Plug in the given values: Q = (54.0g * 334 J/g) + (54.0g * 4.18 J/g°C * (12.5°C - 0°C))
3. Set up an equation to find the mass of iron needed to produce the desired final temperature:
- The total heat gained by the water and the ice is equal to the total heat lost by the iron:
- Q_iron = Q_water + Q_ice
- Substitute the previously calculated values and the unknown mass of iron into the equation.
4. Solve the equation for the unknown mass of iron.
By following these steps, you will be able to determine the mass of iron needed to produce the desired final temperature.