Question

what mass of ethanol will release 410.0 j of heat when it cools from 32.2°c to 19.1°c? the specific heat of ethanol is 2.44 j/g°c. a 12.8 g b 76.4 g c 7.49 g d 31.3 g

Explanation:

Step1: Calculate the temperature change

$\Delta T=T_{final}-T_{initial}=19.1^{\circ}C - 32.2^{\circ}C=- 13.1^{\circ}C$

Step2: Use the heat - mass - specific heat formula

The formula for heat $q = mc\Delta T$, where $q$ is the heat, $m$ is the mass, $c$ is the specific heat, and $\Delta T$ is the temperature change. We want to find $m$, so we can rewrite the formula as $m=\frac{q}{c\Delta T}$. Given $q=-410.0\ J$ (negative because heat is released), $c = 2.44\ J/g^{\circ}C$, and $\Delta T=-13.1^{\circ}C$.
Substitute the values into the formula: $m=\frac{- 410.0\ J}{2.44\ J/g^{\circ}C\times(-13.1^{\circ}C)}$
First, calculate the denominator: $2.44\times(-13.1)=-31.964$
Then, $m=\frac{-410.0}{-31.964}\approx12.8\ g$

Answer:

A. 12.8 g