Q. 3.106 - An Introduction to General, Organic, and Biological Chemistry

Question

A metal is thought to be copper or gold. When $18g$ of the metal absorbs $58cal$, its temperature rises by $35°C$. $(3.6)$

a. What is the specific heat, in $cal/g °C$, of the metal?

b. Would you identify the metal as copper or gold (see Table 3.11)?

Step-by-Step Solution

Answer

(Part a) The specific heat of the metal is $0.092\frac{\mathrm{cal}}{\mathrm{g}°\mathrm{C}}$.

(Part b) The metal with specific value $0.092\frac{\mathrm{cal}}{\mathrm{g}°\mathrm{C}}$  is copper .

Step1: Given Information (part a)

Given data:$18g$of the metal absorbs $58cal$ of heat, its temperature rises by $35°C$, to find the specific heat of the metal.

Step2: The specific heat, in c a l / g   ° C , of the metal(part a)

The rise in the temperature is $35°C$when the metal absorbs $58cal$ of heat which is$18g$. The specific heat of the metal is calculated with the following equation:

Specific heat(metal) $=$$\frac{\text{ heat }}{\text{ mass }\times \Delta T}$

On the substitution of the respective values we have:  

Specific heat(metal) $=$$\frac{58\mathrm{cal}}{18 \mathrm{g}\times 35°\mathrm{C}}$

                                  $=$$0.092\frac{\mathrm{cal}}{\mathrm{g}°\mathrm{C}}$

The specific heat of the metal is 

$0.092\frac{\mathrm{cal}}{\mathrm{g}°\mathrm{C}}$

Step 3: Given Information(part b)

Given data: $18g$of the metal absorbs $58cal$of heat, its temperature rises by $35°C$, identify the metal as copper or gold.  

Step4: Identification of the metal as copper or gold(part b)

The metal with specific value $0.092\frac{\mathrm{cal}}{\mathrm{g}°\mathrm{C}}$ is copper. (Table 3.11)