Question

what is the final temperature of an ingot of pure nickel with a mass of 177.3 g if it was initially at 22.94°c and 3.36 kj of heat was supplied to the ingot? the molar heat capacity of pure nickel is 26.07 j/(mol·°c). report your answer in °c to 3 sig figs, but do not give units in your answer.

Explanation:

Step1: Calculate the number of moles of nickel

The molar mass of nickel (\(Ni\)) is \(M = 58.69\space g/mol\).
The number of moles \(n=\frac{m}{M}\), where \(m = 177.3\space g\)
\(n=\frac{177.3}{58.69}\space mol\approx 3.02\space mol\)

Step2: Use the heat - capacity formula

The heat - capacity formula is \(q=nC\Delta T\), where \(q = 3360\space J\) (since \(3.36\space kJ=3360\space J\)), \(C = 26.07\space J/(mol\cdot^{\circ}C)\), and \(\Delta T=T_{final}-T_{initial}\)
We can rewrite the formula for \(\Delta T\): \(\Delta T=\frac{q}{nC}\)
Substitute \(n = 3.02\space mol\), \(C = 26.07\space J/(mol\cdot^{\circ}C)\), \(q = 3360\space J\)
\(\Delta T=\frac{3360}{3.02\times26.07}\)
\(\Delta T=\frac{3360}{78.7314}\approx42.7\space^{\circ}C\)

Step3: Calculate the final temperature

Since \(\Delta T=T_{final}-T_{initial}\), and \(T_{initial}=22.94\space^{\circ}C\)
\(T_{final}=\Delta T + T_{initial}\)
\(T_{final}=42.7+22.94 = 65.6\space^{\circ}C\)

Answer:

65.6