What time is required for 100 g of reactant to reduce to 25 g in a first order reaction having half life 5760 year?

Step-by-step solution

For a first order reaction, aligned & [ A ₀ ]=100 ~g ; [ A _ t ]=25 ~g ; t _ 1 / 2 =5760 years & k = 0.693 t _ 1 / 2 = 0.693 5760 yr =1.203 10⁻⁴ year ⁻¹ & t = 2.303 k ₁₀ [ ~A ₀ ] [ A _ t ] & t = 2.303 1.203 10⁻⁴ year ⁻¹ ₁₀ 100 25 & =19141.8 0.6021=11526.5 years aligned