Question

when 1711 j of heat energy is added to 45.0 g of ethanol, c₂h₆o, the temperature increases by 15.5 °c. calculate the molar heat capacity of c₂h₆o. cp = j/(mol·°c)

Explanation:

Step1: Calculate the number of moles of ethanol

The molar mass of \(C_2H_6O\) is \(M=(2\times12.01 + 6\times1.008+16.00)\space g/mol=46.07\space g/mol\).
The number of moles \(n=\frac{m}{M}\), where \(m = 45.0\space g\). So \(n=\frac{45.0\space g}{46.07\space g/mol}\approx0.977\space mol\).

Step2: Use the heat - capacity formula

The heat formula is \(q = C_p\times n\times\Delta T\), where \(q = 1711\space J\), \(n\) is the number of moles, and \(\Delta T=15.5^{\circ}C\).
We need to solve for \(C_p\), so \(C_p=\frac{q}{n\times\Delta T}\).
Substitute \(q = 1711\space J\), \(n = 0.977\space mol\), and \(\Delta T = 15.5^{\circ}C\) into the formula:
\(C_p=\frac{1711\space J}{0.977\space mol\times15.5^{\circ}C}\)
First, calculate \(0.977\times15.5 = 15.1435\).
Then \(C_p=\frac{1711}{15.1435}\space J/(mol\cdot^{\circ}C)\approx113\space J/(mol\cdot^{\circ}C)\)

Answer:

\(113\space J/(mol\cdot^{\circ}C)\)