Question

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

The concentration of NaCl is 0.118 M at the start of the reaction, and 0.0900 M after 118 seconds. The initial concentrations of the products are zero.

The average rate of reaction (in M/min) over this time period- 1.42×10^-2 M/min

What is the average rate of change (in M/min) of NaCl in the first 118 seconds and what is the average rate of change (in M/min) of NaNO₃ in the first 118 seconds?

I keep getting 0.000237 M/min but it's wrong?

Answer 1

Rate of reaction is rate of change of concentration of reactant or rate of change of concentration of product with time. Since rate of reaction depends on concentration, it changes continuously as reaction proceeds. The rate of change in concentration of reactant or of product in unit time or over a given interval of time is the average rate of reaction for that interval of time.

For a reaction such as,   aA + bB ​ cC + dD

Rate of reaction, dx / dt is given by,

(dx / dt ) = - (1/a)*(dA / dt ) = - (1/b)*(dB / dt ) = (1/c)*(dC / dt ) = (1/d)*(dD / dt )   

where, (dA / dt ), (dB / dt ), (dC / dt )​, (dD / dt )​ are rates of change of concentrations of A, B, C and D respectively.

Since concentrations of reactants, A and B, decrease as reaction proceeds, (-) sign is used in above equation when relating rate of reaction and rate of change in concentration of reactant.

The given reaction is, AgNO₃ (aq) + NaCl (aq) ​  AgCl (aq) + NaNO₃ (aq)

The above equation is balanced and the stoichiometric coefficient is 1 for any reactant and for any product in the above balanced chemical equation. Hence,

(average rate of reaction i.e dx/dt) = - (average rate of change in concentration of reactant i.e d[reactant] / dt)

= +(average rate of change in concentration of product i.e d[product] / dt)

Given, (average rate of reaction)​ = 1.42 * 10^-2 M/min

Hence, (average rate of reaction)​ = 1.42 * 10^-2 M/min

= - (average rate of change in concentration of NaCl, a reactant)

= +(average rate of change in concentration of NaNO₃, a product)

Therefore, (average rate of change in concentration of NaCl, a reactant)​ = - (average rate of reaction)

= - (1.42 * 10^-2 M/min) = - 1.42 * 10^-2 M/min

and (average rate of change in concentration of NaNO₃, a product) = (average rate of reaction)

= 1.42 * 10^-2 M/min

Answer:

In the first 118 seconds,

average rate of change in concentration of NaCl​ is - 1.42 * 10^-2 M/min​

​and average rate of change in concentration of NaNO₃ ​ is + 1.42 * 10^-2M/min​