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Question

For one mole of an ideal gas, the slope of $$V$$ versus $$T$$ curve at a constant pressure of $$2\ atm$$ is $$X\ L\ mol^{-1}K^{-1}$$. The value of the ideal universal gas constant $$R$$ in terms of $$X$$ is:


A
X L atm mol1K1
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B
X2 L atm mol1K1
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C
2X L atm mol1K1
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D
2X atm L1 mol1K1
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Solution

The correct option is C $$2X\ L\ atm\ mol^{-1}K^{-1}$$
At constant pressure and same number of moles, Volume of the gas is the directly proportional to the temperature of the gas. The slope of V versus T graph i.e slope=$$\dfrac{\Delta V}{\Delta T}$$=$${\text{X}}$$ $$L{mol}^{-1}{K}^{-1}$$
But, $$\dfrac{\Delta V}{\Delta T}$$=$$\dfrac{R}{P}$$ (no. of moles = 1)
Now, $$P=2$$
Therefore, $$R$$=$$2{\text{X}}$$ $${\text{L atm}}$$ $${mol}^{-1}{K}^{-1}$$

Chemistry

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