Question

A 63.5 g sample of an unidentified metal absorbs 355 J of heat when its temperature changes by 4.56°C. Calculate the specific heat capacity of the metal.

A) 1.08 J/g°C
B) 2.45 J/g°C
C) 6.12 J/g°C
D) 15.53 J/g°C

Answer 1

Calculating the specific heat capacity involves using the formula where Q = mcΔT to solve for c by rearranging the equation to c = Q / (mΔT). Plugging in the values from the question gives a specific heat capacity of 1.226 J/g°C, which does not match any of the provided multiple-choice options. Double-checking for any possible mistakes or typos in the given data is recommended.

Step-by-step explanation:

To calculate the specific heat capacity of the metal, we use the formula which relates heat absorbed to the mass, specific heat capacity, and the temperature change:

Q = mcΔT

Where:
Q = heat absorbed (in Joules),
m = mass of the substance (in grams),
c = specific heat capacity (in J/g°C),
ΔT = change in temperature (in °C).

Rearranging the formula to solve for c gives us:

c = Q / (mΔT)

Plugging in the known values:

c = 355 J / (63.5 g · 4.56°C)

c = 355 J / (289.56 g°C)
Therefore, the specific heat capacity is:

c = 1.226 J/g°C

However, this value does not match any of the given multiple-choice options. We should double-check the calculation to ensure there is no error.

Calculating again for clarity:

355 J / (63.5 g · 4.56°C) = 1.226 J/g°C (the same result).

Since the calculated value does not match any of the options, there may be an error in the given choices, the question itself, or the calculation we have performed. Referring to the original question for any possible typos or mistakes is advised. If no error is found, the student should be notified about the discrepancy.