Question

learning goal: to understand the concepts of heat capacity, specific heat, and molar heat capacity. heat capacity, c, is the amount of energy required to raise the temperature of a substance by exactly one degree celsius. the energy needed to warm an object increases as the mass of that object increases. we see this in our everyday life. for example, we know that it takes more energy to heat a large tank of water than a small cup. because of this dependence on mass, experimentally - determined heat capacities are always reported in terms of the amount of the substance that is heated. one method is to report how much energy it takes to raise the temperature of one mole of a substance by exactly one degree celsius. this value is the molar heat capacity, which has the symbol (c_p). the molar heat capacity is given in the units (jcdot mol^{-1}cdot ^{circ}c^{-1}). a second method is to report how much energy it takes to raise the temperature of one gram of a substance by exactly one degree celsius. this value is the specific heat, which has been given the symbol (c_s). the units for specific heat are (jcdot g^{-1}cdot ^{circ}c^{-1}). the heat capacity of a substance is therefore related to the energy needed to raise its temperature by an amount (delta t). that is, (q = nc_pdelta t), where (n) denotes the number of moles of the substance, or (q = mc_sdelta t), where (m) denotes the number of grams of the substance.

part a
it takes 50.0 j to raise the temperature of an 10.7 g piece of unknown metal from (13.0^{circ}c) to (24.2^{circ}c). what is the specific heat for the metal?
express your answer with the appropriate units.

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c_s=

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parts b and c
the next two questions pertain to silver. they have nothing to do with unknown metal described in part a.

part b
the molar heat capacity of silver is (25.35 jcdot mol^{-1}cdot ^{circ}c^{-1}). how much energy would it take to raise the temperature of 10.7 g of silver by (14.2^{circ}c)?
express your answer with the appropriate units.

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q=

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Explanation:

Step1: Recall the heat - capacity formula

The formula for heat energy is $q = mC_s\Delta T$, where $q$ is the heat energy, $m$ is the mass, $C_s$ is the specific heat, and $\Delta T$ is the change in temperature. For Part A, we can re - arrange the formula to solve for $C_s$: $C_s=\frac{q}{m\Delta T}$.

Step2: Calculate $\Delta T$ for Part A

$\Delta T=T_2 - T_1$. Given $T_1 = 13.0^{\circ}C$ and $T_2 = 24.2^{\circ}C$, then $\Delta T=(24.2 - 13.0)^{\circ}C=11.2^{\circ}C$. The mass $m = 10.7g$ and $q = 50.0J$.
Substitute into the formula for $C_s$: $C_s=\frac{50.0J}{10.7g\times11.2^{\circ}C}\approx0.420J\cdot g^{-1}\cdot^{\circ}C^{-1}$.

Step3: For Part B, first convert mass to moles

The molar mass of silver ($Ag$) is $M = 107.87g/mol$. The number of moles $n$ of silver with mass $m = 10.7g$ is $n=\frac{m}{M}=\frac{10.7g}{107.87g/mol}\approx0.0992mol$.

Step4: Use the molar - heat - capacity formula for Part B

The formula for heat energy using molar heat capacity is $q = nC_p\Delta T$. Given $C_p = 25.35J\cdot mol^{-1}\cdot^{\circ}C^{-1}$, $n = 0.0992mol$, and $\Delta T = 14.2^{\circ}C$.
Then $q=0.0992mol\times25.35J\cdot mol^{-1}\cdot^{\circ}C^{-1}\times14.2^{\circ}C\approx35.4J$.

Answer:

Part A: $C_s = 0.420J\cdot g^{-1}\cdot^{\circ}C^{-1}$
Part B: $q = 35.4J$