Question 21fd7

Sep 21, 2017

$\text{0.434 moles Cu}$

Explanation:

The key here is the specific heat of copper, which tells you the amount of energy needed to increase the temperature of $\text{1 g}$ of copper by ${1}^{\circ} \text{C}$.

${c}_{\text{Cu" = "0.385 J g"^(-1)""^@"C}}^{- 1}$

This tells you that in order to increase the temperature of $\text{1 g}$ of copper by ${1}^{\circ} \text{C}$, you need to provide the sample with $\text{0.385 J}$ of heat.

Now, you know that you supplied a total of $\text{280.0 J}$ of heat to your sample and that its temperature increased by ${26.4}^{\circ} \text{C}$.

Use the specific heat of the sample to find the heat needed to increase the temperature of copper by ${26.4}^{\circ} \text{C}$.

26.4 color(red)(cancel(color(black)(""^@"C"))) * overbrace("0.385 J"/("1 g" * 1 color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("the specific heat of copper")) = "10.164 J g"^(-1)

This tells you that in order to increase the temperature of $\text{1 g}$ of copper by ${26.4}^{\circ} \text{C}$, you need $\text{10.164 J}$ of heat.

You can thus say that the mass of the sample is equal to

280.0 color(red)(cancel(color(black)("J"))) * overbrace("1 g"/(10.164color(red)(cancel(color(black)("J")))))^(color(blue)("for a 26.4-"""^@"C increase")) = "27.55 g"#

Finally, to convert this to moles, use the molar mass of copper

$27.55 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) * "1 mole Cu"/(63.546color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("0.434 moles Cu}}}}$

The answer is rounded to three sig figs.