# A sample of nitrogen dioxide gas occupies 625 cm^3 at 70.0 °C and 15.0 psi. What is the final Celsius temperature if the volume is 545 cm^3 at 15.0 psi?

Dec 27, 2016

The final temperature in degrees Celsius is $\text{25.9"^@"C}$.

#### Explanation:

Since the pressure and amount of gas is held constant, you can use Charles' law, the volume-temperature law, which states that at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature. This means that as the volume increases, the temperature increases, and vice versa.

The initial calculation will require the conversion of the Celsius temperature to Kelvins. After the calculation is complete, the new temperature will be converted from Kelvins back to degrees Celsius.

Equation

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$, where $V$ is volume in $\text{cm"^3}$, and $T$ is temperature in Kelvins

Known
${V}_{1} = \text{625 cm"^3}$
${T}_{1} = \text{70.0"^@"C"+273.15="343.15 K}$
${V}_{2} = \text{545 cm"^3}$

Unknown
${T}_{2}$

Solution
Rearrange the equation to isolate ${T}_{2}$. Substitute the known values into the equation and solve.

${T}_{2} = \frac{{V}_{2} {T}_{1}}{V} _ 1$

T_2=(545"cm"^3xx343.15"K")/(625"cm"^3)="299 K"

Final temperature in degrees Celsius

$\text{299 K"-"273.15"="25.9"^@"C}$ rounded to three significant figures