# The molar heat capacity of silver is 25.35 J/mol*C. How much energy would it take to raise the temperature of 10.2 g of silver by 14.0 degrees C?

Apr 16, 2018

$33.6 J$

#### Explanation:

You have to use q=mCΔT
$m = 10.2 g$
$C = 25.35$ (J/mol)*C
$T = 14 C$
First convert $10.2$ to moles by dividing it by the molar mass of silver
$\frac{10.2}{107.8682} = .0945598425$
Than plug into equation
$q = \left(.0945598425 m o l\right) \left(25.35\right) \left(14\right)$
$q = 33.6 J$

Apr 17, 2018

Around $33.6$ joules

#### Explanation:

We use the specific heat equation, which states that,

$q = m c \Delta T$

• $m$ is the mass of the object

• $c$ is the specific heat capacity of the object

• $\Delta T$ is the change in temperature

We got: $m = 10.2 \setminus \text{g", c=(25.35 \ "J")/("mol" \ ""^@"C"),DeltaT=14""^@"C}$.

So, let's first convert that amount of silver into moles.

Silver has a molar mass of $107.8682 \setminus \text{g/mol}$. So here, we got:

(10.2color(red)cancelcolor(black)"g")/(107.8682color(red)cancelcolor(black)"g""/mol")=0.0945598425 \ "mol"

I will keep this number and I'll round off at the end.

So, the heat needed is:

q=0.0945598425color(red)cancelcolor(black)"mol"*(25.35 \ "J")/(color(red)cancelcolor(black)"mol"color(red)cancelcolor(black)(""^@"C"))*14color(red)cancelcolor(black)(""^@"C")

$\approx 33.6 \setminus \text{J}$