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  4. What is the pressure of 2 mole of NH3 at 27°C when its volume is 5 lit. in van der Waals equation (a = 4.17, b = 0 .03711)

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Q. What is the pressure of 2 mole of $NH_3$ at 27$^\circ$C when its volume is 5 lit. in van der Waals equation (a = 4.17, b = 0 .03711)

Odisha JEEOdisha JEE 2004States of Matter

Solution:

T = 27 + 273 = 300 K.
R = 0.082 L atm $K^{-1} \, mol^{-1}$
n = 2 mol, a = 4.17
V = 5 L b = 0.03711
$\left(P + \frac{an^2}{V^2} \right) $ (V - nb) = nRT
$\left(P + \frac{4.17 \times 2^2}{5^2} \right) (5 -2 \times 0.3711) = 2 \times 0.0821 \times 300 $
$\left(P + \frac{4.17 \times 4}{25} \right) (5 - 0.07422) = 600 \times 0.0821$
(P + 0.67) (4-93) = 600 $\times$ 0.0821
P + 0.67 = $\frac{600 \times 0.0821}{4.93}$
P + 0.67 = 9.99
P = 9.99 - 0.67 = 9.32 atm