A certain substance has a mass per mole of 47 g/mol. When 312 J is added as heat to a 34.0 g sample, the sample's temperature rises from 24.0°C to 44.0°C. What are the (a) specific heat and (b) molar specific heat of this substance? (c) How many moles are present?

(a) 0.459 Jg⁻¹°C⁻¹

(b) 22 Jmol⁻¹°C⁻¹

(c) 0.72 moles

Explanation:

(a) The specific heat capacity can be calculated using the following equation:

Q = mcΔt, where Q is the heat energy, m is the mass, c is the specific heat capacity, and Δt is the temperature change from initial to final.

Rearranging the equation to solve for c gives:

c = Q / (mΔt) = (312J) / ((34.0g) (44.0°C - 24°C) = 0.459 Jg⁻¹°C⁻¹

(b) To find the molar specific heat, grams in the above result must be converted to moles using the mass per mole:

(0.459 Jg⁻¹°C⁻¹) (47g/mol) = 22 Jmol⁻¹°C⁻¹

(c) The numer of moles present are found by converting grams to moles using the mas per mole:

(34.0g) (mol/47g) = 0.72 moles