Question

Question #21fd7

Answer 1

`"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 `"1 g"` of copper by `1^@"C"`.

`c_"Cu" = "0.385 J g"^(-1)""^@"C"^(-1)`

This tells you that in order to increase the temperature of `"1 g"` of copper by `1^@"C"`, you need to provide the sample with `"0.385 J"` of heat.

Now, you know that you supplied a total of `"280.0 J"` of heat to your sample and that its temperature increased by `26.4^@"C"`.

Use the specific heat of the sample to find the heat needed to increase the temperature of copper by `26.4^@"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 `"1 g"` of copper by `26.4^@"C"`, you need `"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 color(red)(cancel(color(black)("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.