# For an equilibrium reaction, how can K_c, and K_P be related?

Nov 29, 2015

${K}_{c}$, requires units of concentration in $m o l \cdot {L}^{-} 1$; ${K}_{p}$ units pressure. The constants can be related.

#### Explanation:

For the reaction,
$A + B r i g h t \le f t h a r p \infty n s C + D$, we can write the equilibrium constant in terms of concentration, $m o l \cdot {L}^{-} 1$:
${K}_{c}$ $=$ $\frac{\left[C\right] \left[D\right]}{\left[A\right] \left[B\right]}$

Note that ${K}_{c}$ is dimensionless. Should the reaction be in the gas phase, then we can utilize the Ideal Gas Law: $P V = n R T$, or $\frac{n}{v} = \frac{P}{R T}$. Dalton's Law of partial pressures holds that the pressure exerted by a component in a gaseous mixtures is the same as the pressure it would exert if it alone occupied the container, thus,

${n}_{A} / v = {P}_{A} / \left(R T\right)$; ${n}_{B} / v = {P}_{B} / \left(R T\right)$ etc.

And ${K}_{P}$ $=$ $\frac{\left[{P}_{C}\right] \left[{P}_{D}\right]}{\left[{P}_{A}\right] \left[{P}_{b}\right]}$ $=$ ${K}_{c} / \left(R T\right)$

Reasonably, ideal gas behavious is assumed. So, the units can be in $m o l \cdot {L}^{-} 1$.