Question

From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants.

1. 3NO(g) \(\to\) N₂O (g) Rate = k[NO]₂
2. H₂O₂ (aq) + 3I⁻(aq) + 2H⁺ \(\to\) 2H₂O(l) + I₃^-  Rate = k[H₂O₂][I⁻]
3. CH₃CHO(g) \(\to\) CH₄(g) + CO(g)  Rate = k [CH₃CHO]\(\frac 32\)
4. C₂H₅Cl(g) \(\to\) C₂H₄(g) + HCl(g)  Rate = k [C₂H₅Cl]

Answer 1

(i) Given rate = k [NO]₂
Therefore, order of the reaction = 2
Dimension of \(K =\frac {Rate }{ [NO]^2}\)
\(= \frac {mol L^{-1} s^{-1}}{(mol L^{-1})^2}\)
\(= \frac {mol L^{-1} s^{-1}}{mol^2 L^{-2}}\) 
\(= L \ mol^{-1} s^{-1}\)

---

(ii) Given rate = k [H₂O₂] [I⁻]
Therefore, order of the reaction = 2
Dimension of \(K = \frac {Rate}{[H_2O_2][I^-]}\)
= \(\frac {mol L^{-1} s^{-1}}{(mol L^{-1})(mol L^{-1})}\)
= \(L\  mol^{-1} s^{-1}\)

---

(iii) Given rate = \(k [CH_3CHO]^{\frac 32}\)
Therefore, order of reaction =\(\frac 32\)
Dimension of \(K = \frac {Rate}{ [CH_3CHO]^{\frac 32}}\)
= \(\frac {mol L^{-1} s^{-1}}{(mol L^{-1})^{\frac 32}}\)
= \(\frac {mol L^{-1} s^{-1}}{mol^{\frac 32} L^{-\frac 32}}\)
= \(L^{\frac 12} mol^{-\frac 12} s^{-1}\)

---

(iv) Given rate = \(k [C_2H_5Cl]\)
Therefore,order of the reaction = 1
Dimension of \(k = \frac {Rate}{ [C_2H_5Cl]}\)
= \(\frac {mol L^{-1} s^{-1}}{(mol L^{-1})}\)
= \(s^{-1}\)