Chapter 14.3, Problem 37PP

Interpretation Introduction

Interpretation:

The Pressure is to be calculated on a 1 L sample containing 1.5 g of gas

Concept introduction:

Henry’s Law:

At a given temperature, solubility of the gas in a liquid is directly proportional to the pressure above the liquid:

$\frac{S_1}{P_1}=\frac{S_2}{P_2}$

Where, S represents solubility while P represents pressure.

After cross multiplying, the equation can be written as;

${\mathrm{S}}_1{P}_2=S_2{P}_1$

Where

S₁ = Solubility of gas

S₂ = Solubility at new pressure

P₁ = Initial Pressure

P₂ = New Pressure

Answer to Problem 37PP

The Pressure is 23 atm on a 1 L sample containing 1.5 g of gas.

Given information:

Mass of gas=1.5g

Volume=1 L

Solubility of gas S₁=0.66g/L

P₁₌10atm

Calculation:

At a given temperature, solubility of the gas in a liquid is directly proportional to the pressure above the liquid:

$\frac{S_1}{P_1}=\frac{S_2}{P_2}$

Where, S represents solubility while P represents pressure.

After cross multiplying, the equation can be written as;

$S_1{P}_2=S_2{P}_1$

Where,

S₁ = Solubility of gas

S₂ = Solubility at new pressure

P₁ = Initial Pressure

P₂ = New Pressure

Write the formula for solubility of gas:

$\begin{array}{c}Solubilityofgas\left({\mathrm{S}}_2\right)=\frac{Mass}{Volume}\\ =\frac{1.5}{1}\\ =1.5\mathrm{g}/L\end{array}$

From the equation, ${\mathrm{S}}_1{P}_2=S_2{P}_1$

P₂₌$\frac{S_2\times P_1}{S_1}$

Putting all the values in the equation:

$\begin{array}{l}=\frac{1.5\times 10}{0.6}\\ = 23atm\end{array}$

So, The Pressure is 23 atm on a 1 L sample containing 1.5 g of gas.

Explanation of Solution

Given information:

Mass of gas=1.5g

Volume=1 L

Solubility of gas S₁=0.66g/L

P₁₌10atm

Calculation:

At a given temperature, solubility of the gas in a liquid is directly proportional to the pressure above the liquid:

$\frac{S_1}{P_1}=\frac{S_2}{P_2}$

Where, S represents solubility while P represents pressure.

After cross multiplying, the equation can be written as;

$S_1{P}_2=S_2{P}_1$

Where,

S₁ = Solubility of gas

S₂ = Solubility at new pressure

P₁ = Initial Pressure

P₂ = New Pressure

Write the formula for solubility of gas:

$\begin{array}{c}Solubilityofgas\left({\mathrm{S}}_2\right)=\frac{Mass}{Volume}\\ =\frac{1.5}{1}\\ =1.5\mathrm{g}/L\end{array}$

From the equation, ${\mathrm{S}}_1{P}_2=S_2{P}_1$

P₂₌$\frac{S_2\times P_1}{S_1}$

Putting all the values in the equation:

$\begin{array}{l}=\frac{1.5\times 10}{0.6}\\ = 23atm\end{array}$

So, The Pressure is 23 atm on a 1 L sample containing 1.5 g of gas.