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The molar heat capacity of silver is $\dfrac{{25.35J}}{{mo{l^ \circ }C}}$. How much energy would it take to raise the temperature of $10.2g$ of silver by $14.0$ degrees $C$?

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Last updated date: 13th Jun 2024
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Answer
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Hint:That amount of energy that must be added in the heat form to one mole of substance in order to increase one unit of the temperature is called molar specific heat capacity. Converting the amount of silver into moles will help to bet the answer.

Formula used:
$q = mc\Delta T$
Where, $m$ is the mass, $c$ is the specific heat capacity and $\Delta T$ is the change in the temperature.

Complete step by step answer:
Molar heat capacity is the closely related property of the substances. In which the heat capacity of the sample is divided by the moles of the atom instead of the moles of molecules. That amount of energy that must be added in the heat form to one mole of substance in order to increase one unit of the temperature is called a molar specific heat capacity. It can be calculated as,
$q = mc\Delta T$

We have got the values. The mass is $10.2g$, molar capacity value is $\dfrac{{25.35J}}{{mo{l^ \circ }C}}$. The temperature change is ${14.0^ \circ }C$. Let us convert the amount of silver into moles. The silver has a molar mass $107.8682g/mol$.Divide the values of the mass and the molar mass of the silver.
$\dfrac{{10.2g}}{{107.8682g/mol}}$
Cancel out the common terms gram. We get,
$ \Rightarrow \dfrac{{10.2}}{{107.8682/mol}}$
Divide the terms we get,
$ \Rightarrow 0.0945598425mol$

Keep the number as it is and it can round it off at the end.
The energy required is,
$ \Rightarrow q = 0.0945598425mol.\dfrac{{25.35J}}{{mo{l^ \circ }C}}{.14^ \circ }C$
Cancel out the common terms. The common terms are $mol$ and ${}^ \circ C$. We get,
$ \Rightarrow q = 0.0945598425 \times 25.35 \times 14$
Multiply the above values to get the answer. The answer is
$ \Rightarrow 33.4269043J$
The above value is approximately equal to,
$ \simeq 33.6J$

Therefore, the energy that is required to raise is $33.6J$.

Note:The value of the molar volumes of the solid elements roughly equals constant and therefore the molar heat capacity of the solid is also the same. At the higher end of the heat capacities, the heat capacity will exceed the value of the gas constant.