Question

what is zero order reaction​

Answer 1

EXPLANATION.

Zero order reaction.

A ⇒ Products.

Rate of Reaction [ROR] = r = k[A]⁰.

Rate = r = k (Rate Constant).

Integrate rate law.

A ⇒ Products (99%). [Assume].

Rate = r = -d[A]/dt.

⇒ -d[A]/dt = k[A]⁰.

⇒ d[A] = - kdt.

⇒ dA = -kdt.

$\sf \implies \displaystyle \int_{A_{0}}^{A} dA \ = -\int\limits^t_0 {kdt} \,$

$\sf \implies \bigg[A\bigg]_{A_{0}}^{A} \ = -k \bigg[t \bigg]_{0}^{t}$

⇒ A - A₀ = -k(t - 0).

⇒ A - A₀ = -kt.

⇒ A = A₀ - kt.

A₀ = Initial concentration of A.

A = Concentration of A at any time t.

K = Rate constant.

T = Time in which concentration from A₀ to A.

Half life of reaction Or $\sf (t_{1/2}).$

Time in which reaction completes 50%.

at t = t(1/2).

⇒ A = A₀/2.

⇒ A = A₀ - kt.

$\sf \implies \dfrac{A_{0}}{2} = A_{0} - kt_{1/2}$

$\sf \implies kt_{1/2} = A_{0}/2$

$\sf \implies t_{1/2} = A_{0}/2k$

Life time of reaction.

Time in which 100% reaction complete.

$\sf \implies t = t_{f}$

⇒ A = 0.

⇒ A = A₀ - kt.

⇒ 0 = A₀ - kt(f).

⇒ t(f) = A₀/k.

Answer 2

Zero order reaction.

A ⇒ Products.

Rate of Reaction [ROR] = r = k[A]⁰.

Rate = r = k (Rate Constant).

Integrate rate law.

A ⇒ Products (99%). [Assume].

Rate = r = -d[A]/dt.

⇒ -d[A]/dt = k[A]⁰.

⇒ d[A] = - kdt.

⇒ dA = -kdt.

$\tiny\sf \implies \displaystyle \int_{A_{0}}^{A} dA \ = -\int\limits^t_0 {kdt} \,⟹∫ </h2><p>A </p><p>0</p><p> </p><p> </p><p>A</p><p> </p><p> dA =− </p><p>0</p><p>∫</p><p>t</p><p> </p><p> kdt$

$\sf \implies \bigg[A\bigg]_{A_{0}}^{A} \ = -k \bigg[t \bigg]_{0}^{t}⟹[A] </p><p>A </p><p>0</p><p> </p><p> </p><p>A</p><p> </p><p> =−k[t] </p><p>0</p><p>t$

⇒ A - A₀ = -k(t - 0).

⇒ A - A₀ = -kt.

⇒ A = A₀ - kt.

A₀ = Initial concentration of A.

A = Concentration of A at any time t.

K = Rate constant.

T = Time in which concentration from A₀ to A.

Half life of reaction Or

$\sf (t_{1/2}).(t </p><p>1/2</p><p> </p><p> ).$

Time in which reaction completes 50%.

at t = t(1/2).

⇒ A = A₀/2.

⇒ A = A₀ - kt.

$\sf \implies \dfrac{A_{0}}{2} = A_{0} - kt_{1/2}⟹ </p><p>2</p><p>A </p><p>0</p><p> </p><p> </p><p> </p><p> =A </p><p>0</p><p> </p><p> −kt </p><p>1/2$

$\sf \implies kt_{1/2} = A_{0}/2⟹kt </p><p>1/2</p><p> </p><p> =A </p><p>0</p><p> </p><p> /2$

$\sf \implies t_{1/2} = A_{0}/2k⟹t </p><p>1/2</p><p> </p><p> =A </p><p>0</p><p> </p><p> /2k$

Life time of reaction.

Time in which 100% reaction complete.

$\sf \implies t = t_{f}⟹t=t </p><p>f$

⇒ A = 0.

⇒ A = A₀ - kt.

⇒ 0 = A₀ - kt(f).

⇒ t(f) = A₀/k.