Chapter 7, Problem 7.35EP

(a)

Interpretation Introduction

Interpretation:

The volume in liters for a sample of carbon dioxide gas at given set of conditions by using combined gas law has to be determined.

Concept Introduction:

Combined gas law tells that the Kelvin temperature of gas is directly proportional to the pressure and volume of a fixed amount of gas.  The mathematical expression for combined gas law can be represented as follows,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Explanation of Solution

Record the given data,

$\begin{array}{l}{P}_1=1.35atm\\ V_1=15.2L\\ T_1=33°Cconvertedto306K\\ P_2=3.50atm\\ T_2=35°Cconvertedto308K\\ V_2=?\end{array}$

Now, substitute these values in rearranged combined gas law and do some simple mathematical calculation to gent final answer as follows,

$V_2=V_1\times \frac{P_1}{P_2}\times \frac{T_2}{T_1}$

$V_2=15.2L\times \left(\frac{1.35atm}{3.50atm}\right)\times \left(\frac{308K}{306K}\right)=5.90L$

The final volume in liters for a sample of carbon dioxide gas at given set of conditions is $5.90L.$

(b)

Interpretation Introduction

Interpretation:

The pressure in atmospheres for a sample of carbon dioxide gas at given set of conditions by using combined gas law has to be determined.

Concept Introduction:

Combined gas law tells that the Kelvin temperature of gas is directly proportional to the pressure and volume of a fixed amount of gas.  The mathematical expression for combined gas law can be represented as follows,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Explanation of Solution

Record the given data,

$\begin{array}{l}{P}_1=1.35atm\\ V_1=15.2L\\ T_1=33°Cconvertedto306K\\ P_2=?\\ T_2=42°Cconvertedto315K\\ V_2=10.0L\end{array}$

Now, substitute these values in rearranged combined gas law and do some simple mathematical calculation to gent final answer as follows,

$P_2=P_1\times \frac{V_1}{V_2}\times \frac{T_2}{T_1}$

$P_2=\text{1}\text{.35 atm}\times \left(\frac{\text{15}\text{.2 L}}{\text{10}\text{.0 L}}\right)\times \left(\frac{\text{315 K}}{\text{306 K}}\right)=2.11atm$

The final pressure in atmosphere for a sample of carbon dioxide gas at given set of conditions is $2.11atm.$

(c)

Interpretation Introduction

Interpretation:

The temperature in degree Celsius for a sample of carbon dioxide gas at given set of conditions by using combined gas law has to be determined.

Concept Introduction:

Combined gas law tells that the Kelvin temperature of gas is directly proportional to the pressure and volume of a fixed amount of gas.  The mathematical expression for combined gas law can be represented as follows,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Explanation of Solution

Record the given data,

$\begin{array}{l}{P}_1=1.35atm\\ V_1=15.2L\\ T_1=33°Cconvertedto306K\\ P_2=7.00atm\\ T_2=?\\ V_2=0.973L\end{array}$

Now, substitute these values in rearranged combined gas law and do some simple mathematical calculation to gent final answer as follows,

$T_2=T_1\times \frac{V_2}{V_1}\times \frac{P_2}{P_1}$

$T_2=306K\times \left(\frac{\text{7}\text{.00}\text{atm}}{\text{1}\text{.35}\text{atm}}\right)\times \left(\frac{\text{0}\text{.973L}}{\text{15}\text{.2L}}\right)=102K$

The obtained pressure is in Kelvin units now we have to convert this value into degree Celsius as follows,

$T-273$

$102-273=-171°C$

The final temperature in degree Celsius for a sample of carbon dioxide gas at given set of conditions is $-171°C.$

(a)

Interpretation Introduction

Interpretation:

The volume in milliliters for a sample of carbon dioxide gas at given set of conditions by using combined gas law has to be determined.

Concept Introduction:

Combined gas law tells that the Kelvin temperature of gas is directly proportional to the pressure and volume of a fixed amount of gas.  The mathematical expression for combined gas law can be represented as follows,

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

Explanation of Solution

Record the given data,

$\begin{array}{l}{P}_1=1.35atm\\ V_1=15.2Lconvertedto15200mL\\ T_1=33°Cconvertedto306K\\ P_2=6.70atm\\ T_2=97°Cconvertedto370K\\ V_2=?\end{array}$

Now, substitute these values in rearranged combined gas law and do some simple mathematical calculation to gent final answer as follows,

$V_2=V_1\times \frac{P_1}{P_2}\times \frac{T_2}{T_1}$

$V_2=15200mL\times \left(\frac{1.35atm}{6.70atm}\right)\times \left(\frac{370K}{306K}\right)=3.70\times {10}^{3}mL$

The final volume in liters for a sample of carbon dioxide gas at given set of conditions is $3.70\times {10}^{3}mL.$