For the reaction

SO_{2} + \(\frac{1}{2}\) O_{2} ⇌ SO_{3}

Given, K_{c} = 61.7

T = 600 + 273 = 873K

∆n = No. of moles of product - No. of moles of Reactants

= 1 − (1 + \(\frac{1}{2}\) )

= − \(\frac{1}{2}\)

∴ K_{p} = K_{c} (RT)^{∆}

= 61.7(0.0821 × 873)^{−\(\frac{1}{2}\) }

= 7.29

K_{p} = \(\frac{(P_{SO_3})}{(P_{SO_2}).(P_{O_2})^{\frac{1}{2}}}\)

= \(\frac{atm}{atm.(atm)^{\frac{1}{2}}}\)

= \(atm^{-\frac{1}{2}}\)

∴ The unit of Kp for the above equilibrium is \(atm^{-\frac{1}{2}}\)