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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.
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♦ Relevant knowledge
The condition of a gas is defined by its temperature as well as pressure, volume and the quantity of moles present in the gas. These parameters are linked to each other through an empirical law, known by the Ideal Gas Law. This law is a blend of Boyle’s Law as well as Charle’s Law and Gay-Lussac’s Law as well as Avogadro’s Law. In any state the ideal gas will follow an ideal gas formula.
Ideal gas equation is the solution to the problem.
First, calculate the pressure value at each point of the graph using the ideal gas equation. Next, compare pressures at each point to rank them from highest to lowest.
The ideal gas equation is the following:
[katex]PV = nRT[/katex]
n is the number of moles in a gas and R is the constant.
This expression calculates the pressure at point A.
[katex]{P_{\rm{A}}}{V_{\rm{A}}} = nR{T_{\rm{A}}}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_{\rm{A}}} = nR\frac{{{T_{\rm{A}}}}}{{{V_{\rm{A}}}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{A}}} = nR\frac{{2\,{\rm{units}}}}{{3\,{\rm{units}}}}\\\\ = \left( {0.666} \right)nR\\\end{array}[/katex]
This expression calculates the pressure at point A.
[katex]{P_{\rm{B}}}{V_{\rm{B}}} = nR{T_{\rm{B}}}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_{\rm{B}}} = nR\frac{{{T_{\rm{B}}}}}{{{V_{\rm{B}}}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{B}}} = nR\frac{{2\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( {0.333} \right)nR\\\end{array}[/katex]
This expression calculates the pressure at point B.
[katex]{P_{\rm{C}}}{V_{\rm{C}}} = nR{T_{\rm{C}}}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_{\rm{C}}} = nR\frac{{{T_{\rm{C}}}}}{{{V_{\rm{C}}}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{C}}} = nR\frac{{4\,{\rm{units}}}}{{3\,{\rm{units}}}}\\\\ = \left( {1.333} \right)nR\\\end{array}[/katex]
This expression calculates the pressure at point D.
[katex]{P_{\rm{D}}}{V_{\rm{D}}} = nR{T_{\rm{D}}}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_{\rm{D}}} = nR\frac{{{T_{\rm{D}}}}}{{{V_{\rm{D}}}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{D}}} = nR\frac{{4\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( {0.666} \right)nR\\\end{array}[/katex]
This expression calculates the pressure at point E.
[katex]{P_E}{V_E} = nR{T_E}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_E} = nR\frac{{{T_E}}}{{{V_E}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{E}}} = nR\frac{{4\,{\rm{units}}}}{{9\,{\rm{units}}}}\\\\ = \left( {0.444} \right)nR\\\end{array}[/katex]
This expression calculates the pressure at point F.
[katex]{P_{\rm{F}}}{V_{\rm{F}}} = nR{T_{\rm{F}}}[/katex]
n and R are constants.
The following sentence should be rewritten:
[katex]{P_{\rm{F}}} = nR\frac{{{T_{\rm{F}}}}}{{{V_{\rm{F}}}}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{F}}} = nR\frac{{6\,{\rm{units}}}}{{6\,{\rm{units}}}}\\\\ = \left( 1 \right)nR\\\end{array}[/katex]
The rank of points that are highest to lowest pressure can be compared using the graph.
[katex]C > F > A = D > E > B.[/katex]
Ans:
[katex]C > F > A = D > E > B [/katex] is the order of states based on the pressure of gas samples at each point of graph.