Q5.32P - Chemistry: Molecular Nature Of Matter And Change

Question

In preparation for a demonstration, your professor brings a 1.5-L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 85 psi and the temperature in the hall is $\mathbf{23}\mathbf{°}\mathbf{C}$ , how many moles of sulfur dioxide are in the bottle?

Step-by-Step Solution

Answer

The number of moles is 0.418 mol.

Step 1: Ideal gas law

The ideal gas law equation is,

 

 $\mathbf{PV}\mathbf{=}\mathbf{nRT}$

 

The ideal gas law for the given condition can be written as,

 $\mathbf{n}\mathbf{=}\frac{\mathbf{PV}}{\mathbf{RT}}$

 

 

Here,

V is the volume (1.5 L)

T is the temperature ( $\text{23°C\hspace{0.17em}=\hspace{0.17em}}296\text{\hspace{0.17em}K}$ ).

P is the pressure (99.7 psi).

Step 2: Determination of moles.

Firstly we need to change the pressure from psi to atm:

 

 $\mathbf{1}\mathbf{atm}\mathbf{=}\mathbf{14}\mathbf{.6956}\mathbf{psi}$

 

And,

 $\mathbf{99}\mathbf{.7}\mathbf{psi}\mathbf{=}\mathbf{99}\mathbf{.7}\mathbf{psi}\mathbf{\times }\frac{\mathbf{1}\mathbf{atm}}{\mathbf{14}\mathbf{.6956}\mathbf{psi}}\mathbf{=}\mathbf{6}\mathbf{.78}\mathbf{atm}$

 

 

The number of moles of gas in the sample is,

$\begin{array}{l}\mathrm{n}=\frac{\mathrm{PV}}{\mathrm{RT}}\\ \mathrm{n}=\frac{6.78\mathrm{atm}\times 1.5\mathrm{L}}{0.0821{\mathrm{atmLK}}^{-1}{\mathrm{mol}}^{-1}\times 296\mathrm{K}}\\ \mathrm{n}=0.418\mathrm{mol}\end{array}$

Thus, the number of moles is 0.418 mol.