For CO(g) + 2H2(g) CH3OH(g) at 500 K, K_p = 5.0x10^-4 atm^-2. Use R = 0.0821 L atm mol^-1 K^-1 and 1 atm = 1.013 bar. Which statements are correct?

K_c/K_p approx 1.7x10^3 in the units used

K_p approx 5.1x10^-4 bar^-2 when pressures are in bar

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ce092

For $CO (g) + 2 H X_{2} (g) CH X_{3} OH (g)$ at 500 K, $K_{p} = 5.0 \times 1 0^{- 4} at m^{- 2}$ . Use $R = 0.0821 L atm mo l^{- 1} K^{- 1}$ and $1 atm = 1.013 bar$ . Which statements are correct?

Δ n = 1 - 3 = - 2

, so

K_{c} = K_{p} (RT)^{2}

with

RT = 0.0821 \times 500 = 41.05

and

(RT)^{2} = 1685

. Hence

K_{c} = 5.0 \times 1 0^{- 4} \times 1685 = 0.84 L^{2} mo l^{- 2}

and

K_{c} / K_{p} = 1685

, so statements 1 and 2 are true. The units of

K_{c}

are

(L mo l^{- 1})^{2}

, not

mo l^{2} L^{- 2}

. Because

1 atm^{- 2} = (1.013 bar)^{- 2}

K_{p} = 5.0 \times 1 0^{- 4} /1.01 3^{2} = 4.87 \times 1 0^{- 4} ba r^{- 2}

, not

5.1 \times 1 0^{- 4}