Question

Rank the states on the basis of the pressure of the gas sample at each state.

Rank pressure from highest to lowest. To rank items as equivalent, overlap them.

Rank the states on the basis of the pressure of the gas sample at each state. Rank pressure from highest to lowest. To rank items as equivalent, overlap them.

Answer 1

Concepts and reason

The concepts required to solve the given problem is ideal gas equation.

Initially calculate the value of pressure at each point on the graph by using ideal gas equation. Then, compare the pressures at each point and rank the points from highest pressure to lowest pressure.

Fundamentals

The relation between pressure P, absolute temperature T, and volume V of a gas is expressed as Ideal gas equation as follows:

$PV = nRT$

Here, n is number of moles of a gas, and R is the gas constant.

The pressure at point A is calculated by using the following expression:

${P_{\rm{A}}}{V_{\rm{A}}} = nR{T_{\rm{A}}}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_{\rm{A}}} = nR\frac{{{T_{\rm{A}}}}}{{{V_{\rm{A}}}}}$

Substitute ${\rm{3}}\,{\rm{units}}$ for${V_{\rm{A}}}$, $2\,{\rm{units}}$ for ${T_{\rm{A}}}$ the above equation ${P_{\rm{A}}} = nR\frac{{{T_{\rm{A}}}}}{{{V_{\rm{A}}}}}$and solve for ${P_{\rm{A}}}.$

$\begin{array}{c}\\{P_{\rm{A}}} = nR\frac{{2\,{\rm{units}}}}{{3\,{\rm{units}}}}\\\\ = \left( {0.666} \right)nR\\\end{array}$

The pressure at point B is calculated by using the following expression:

${P_{\rm{B}}}{V_{\rm{B}}} = nR{T_{\rm{B}}}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_{\rm{B}}} = nR\frac{{{T_{\rm{B}}}}}{{{V_{\rm{B}}}}}$

Substitute $6\,{\rm{units}}$ for${V_{\rm{B}}}$, $2\,{\rm{units}}$ for ${T_{\rm{B}}}$the above equation ${P_{\rm{B}}} = nR\frac{{{T_{\rm{B}}}}}{{{V_{\rm{B}}}}}$and solve for ${P_{\rm{B}}}.$

$\begin{array}{c}\\{P_{\rm{B}}} = nR\frac{{2\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( {0.333} \right)nR\\\end{array}$

The pressure at point C is calculated by using the following expression:

${P_{\rm{C}}}{V_{\rm{C}}} = nR{T_{\rm{C}}}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_{\rm{C}}} = nR\frac{{{T_{\rm{C}}}}}{{{V_{\rm{C}}}}}$

Substitute $3\,{\rm{units}}$ for${V_{\rm{C}}}$, $4\,{\rm{units}}$ for ${T_{\rm{C}}}$ the above equation ${P_{\rm{C}}} = nR\frac{{{T_{\rm{C}}}}}{{{V_{\rm{C}}}}}$and solve for ${P_{\rm{C}}}.$

$\begin{array}{c}\\{P_{\rm{C}}} = nR\frac{{4\,{\rm{units}}}}{{3\,{\rm{units}}}}\\\\ = \left( {1.333} \right)nR\\\end{array}$

The pressure at point D is calculated by using the following expression:

${P_{\rm{D}}}{V_{\rm{D}}} = nR{T_{\rm{D}}}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_{\rm{D}}} = nR\frac{{{T_{\rm{D}}}}}{{{V_{\rm{D}}}}}$

Substitute $6\,{\rm{units}}$ for${V_{\rm{D}}}$, $4\,{\rm{units}}$ for ${V_{\rm{D}}}$ the above equation ${P_{\rm{D}}} = nR\frac{{{T_{\rm{D}}}}}{{{V_{\rm{D}}}}}$and solve for ${P_{\rm{D}}}.$

$\begin{array}{c}\\{P_{\rm{D}}} = nR\frac{{4\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( {0.666} \right)nR\\\end{array}$

The pressure at point E is calculated by using the following expression:

${P_E}{V_E} = nR{T_E}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_E} = nR\frac{{{T_E}}}{{{V_E}}}$

Substitute $9\,{\rm{units}}$ for${V_E}$, $4\,{\rm{units}}$ for ${T_E}$ the above equation ${P_E} = nR\frac{{{T_E}}}{{{V_E}}}$and solve for ${P_E}.$

$\begin{array}{c}\\{P_{\rm{E}}} = nR\frac{{4\,{\rm{units}}}}{{9\,{\rm{units}}}}\\\\ = \left( {0.444} \right)nR\\\end{array}$

The pressure at point F is calculated by using the following expression:

${P_{\rm{F}}}{V_{\rm{F}}} = nR{T_{\rm{F}}}$

Take n and R as constants.

Rewrite the above expression as follows:

${P_{\rm{F}}} = nR\frac{{{T_{\rm{F}}}}}{{{V_{\rm{F}}}}}$

Substitute $6\,{\rm{units}}$ for${V_{\rm{F}}}$, $6\,{\rm{units}}$ for ${T_{\rm{F}}}$ the above equation ${P_{\rm{F}}} = nR\frac{{{T_{\rm{F}}}}}{{{V_{\rm{F}}}}}$and solve for ${P_{\rm{F}}}.$

$\begin{array}{c}\\{P_{\rm{F}}} = nR\frac{{6\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( 1 \right)nR\\\end{array}$

By comparing the calculate pressures at each point on the graph the rank of points from highest pressure to lowest pressure is given as follows:

$C > F > A = D > E > B.$

Ans:

The order of the states on the basis of the pressure of the gas samples at each point on graph is $C > F > A = D > E > B.$