Final answer:
To find how many grams of iron are needed to absorb 16.0 kJ, we use the formula q = mcΔT. The specific heat (c) for iron is given as approximately 0.449 J/g°C, and the change in temperature (ΔT) is 52°C. However, the calculated value does not match any of the given options, hinting at a possible error.
Step-by-step explanation:
To determine how many grams of iron are needed to absorb 16.0 kJ of heat with a temperature rise from 25°C to 77°C, we can use the formula q = mcΔT, where q is the heat absorbed (in joules), m is the mass of the sample (in grams), c is the specific heat capacity (in J/g°C), and ΔT is the change in temperature.
Given that the specific heat of iron (c) is approximately 0.449 J/g°C, and the ΔT (temperature change) is 77°C - 25°C = 52°C, we can rearrange the formula to solve for m (mass).
First, convert kilojoules to joules: 16.0 kJ = 16,000 J. Then solve for m:
16,000 J = m × 0.449 J/g°C × 52°C
m = 16,000 J / (0.449 J/g°C × 52°C)
m = approximately 690.757 g
However, none of the provided answer choices match this result, indicating that there may be an error in the question or the options provided. If the specific heat value is different than stated, this would change the result accordingly.