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 Figure shows plot of PV/T versus P for $1.00\times {{10}^{-3}}kg$ of oxygen gas at two different temperatures.

A. What does the dotted plot signify ?

B. Which is true: ${{T}_{1}} > {{T}_{2}} or {{T}_{1}} < {{T}_{2}}$ ?

C. What is the value of PV/T where the curves meet on the y-axis ?

D. If we obtained similar plots for $1.00\times {{10}^{-3}}kg$ of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis ? If not, what mass of hydrogen yields the same values of PV/T (for low pressure high temperature region of the plot) ? (Molecular mass of ${{H}_{2}} = 2.02u,\text{ }of\text{ }{{O}_{2}} = 32.0u,\text{ }R = 8.31Jmo{{l}^{-1}}{{K}^{-1}}$)

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Last updated date: 15th Jun 2024
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Answer
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Hint: Ideal gas are those that have no interactions and whose molecules occupy negligible space. These are found to obey the gas laws. Ideal gas equation is PV = nRT.


Complete answer:

A. The dotted plot in the graph shows a straight line, and hence we can say that it depicts the ideal behaviour of gases.

B. ${{T}_{1}} > {{T}_{2}}$ is true. Because, as the temperature increases, it is found that the real gas approach towards ideal behaviour. We can see from the graph that the plot of temperature ${{T}_{1}}$ is close to the ideal behaviour, so we can conclude that ${{T}_{1}} > {{T}_{2}}$.

C. Let’s find out the value of PV/T where the curves meet on the y-axis:

We know that the ideal gas equation is written as: PV = nRT, we can also write it as:

$\frac{PV}{T} = nR$ 

And molecular mass of oxygen is given as 32 g

$nR = \frac{1}{32}\times 8.314$

$nR = 0.256J{{K}^{-1}}$

D. If we obtain similar plots for $1.00\times {{10}^{-3}}kg$ of hydrogen, the same value of PV/T cannot be obtained at the point where the curves meet on the y-axis. This is because for the same amount of hydrogen, it would contain more moles 1 g of oxygen, because of its molar mass.

-We know that the molar mass of hydrogen is equal to 2 g. So, we can say the mass of hydrogen will be:

$m=\frac{PV}{T}\times \frac{M}{R}$

$=0.256\times \frac{2}{8.314}$

$=6.25\times {{10}^{-5}}kg$

- Hence, we can conclude that $6.25\times {{10}^{-5}}kg$ mass of hydrogen yields the same values of PV/T.


Note: We must not forget to write the units after solving any question.

Mostly all the real gases are ideal gases, like hydrogen oxygen etc. Real gases deviate from the ideal behaviour because there is intermolecular force of attraction found in between molecules.