Question

the molar mass of copper is 63.546 g/mol. the specific heat of copper is 0.385
how much heat is released when 0.762 mol of copper cools from
81.6°c to 52.2°c?
a 548 j
b 8.63 j
c 973 j
d 93.7 j

Explanation:

Step1: Calculate the mass of copper

Use the formula \(m = n\times M\), where \(n = 0.762\space mol\) (amount of substance) and \(M=63.546\space g/mol\) (molar mass).
\(m=0.762\times63.546 = 48.422\space g\)

Step2: Calculate the temperature change

Use the formula \(\Delta T=T_{final}-T_{initial}\), where \(T_{initial} = 81.6^{\circ}C\) and \(T_{final}=52.2^{\circ}C\)
\(\Delta T=52.2 - 81.6=- 29.4^{\circ}C\)

Step3: Calculate the heat released

Use the formula \(q = m\times c\times\Delta T\), where \(m = 48.422\space g\), \(c = 0.385\space J/(g\cdot^{\circ}C)\) (specific heat capacity), and \(\Delta T=-29.4^{\circ}C\)
\(q=48.422\times0.385\times(- 29.4)\)
\(q=-548\space J\) (The negative sign indicates heat is released)

Answer:

A. 548 J