A new drug compound is combusted inside a bomb calorimeter containing 541.5 g of water (Mr = 18.0 g mol-1). The temperature of the water increases by 8.39 °C. If the molar heat capacity of water is 75.0 J K-1 mol-1, how much heat is transferred to the water? Input your numerical answer (numbers only) in kJ.

Question

BlackTom AI · Accepted Answer

Heat absorbed by the water equals the molar heat capacity times the number of moles times the temperature change: q = n · C_m · ΔT.

1) Relevant knowledge points and concepts
- Molar heat capacity C_m (J K^-1 mol^-1) relates heat absorbed per mole per degree: q = n·C_m·ΔT.
- Number of moles n = mass / molar mass.
- Temperature change in °C is equivalent to K for ΔT.
- Convert final energy from J to kJ (1 kJ = 1000 J).

2) Step-by-step reasoning
- Find moles of water from its mass and molar mass.
- Multiply moles by molar heat capacity to get total heat capacity of the sample.
- Multiply total heat capacity by ΔT to get heat absorbed (in J).
- Convert to kJ and round appropriately.

3) Calculations with intermediate steps
- n = mass / M_r = 541.5 g / 18.0 g mol^-1 = 30.083333... mol
- Total heat capacity of the water sample = n · C_m = 30.083333... mol × 75.0 J K^-1 mol^-1 = 2256.25 J K^-1
- Heat absorbed q = (total heat capacity) × ΔT = 2256.25 J K^-1 × 8.39 K = 2256.25 × 8.39 = 18,929.9375 J
- Convert to kJ: q = 18,929.9375 J ÷ 1000 = 18.9299375 kJ
- Rounding to three significant figures (consistent with given data like 75.0 and 8.39) yields 18.9 kJ.

4) Why the correct answer is correct
The computation follows directly from the definition of molar heat capacity and correctly converts mass to moles, applies ΔT, and converts units. The small discrepancy you might get using specific heat per gram (4.184 J g^-1 K^-1) is due to round-off differences between C_m = 75.0 J K^-1 mol^-1 and the exact product 18.0×4.184 = 75.312 J K^-1 mol^-1.

5) Other options / common mistakes
- Forgetting to convert grams to moles (using mass directly with molar heat capacity) would be incorrect.
- Omitting the kJ conversion or misplacing decimal points is a frequent error.
- Using an incorrect molar mass or wrong ΔT sign would also lead to wrong answers.

6) Conclusion / final answer confirmation
Following the steps above gives q = 18.9 kJ absorbed by the water. This matches the provided correct answer: 18.9.

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