Under certain conditions the rate of this reaction is zero order in ammonia with a rate constant of ·0.0054Ms−1:→2NH3g+N2g3H2gSuppose a 3.0L ⁢ flask is charged under these conditions with 350.mmol of ammonia. After how much time is there only 175.mmol left? You may assume no other reaction is important.Be sure your answer has a unit symbol, if necessary, and round it to 2 significant digits.

The rate of a zero order reaction is given by the equation:

Rate = k[A]^0

where k is the rate constant and [A] is the concentration of the reactant. Since the reaction is zero order in ammonia, the rate of the reaction is independent of the concentration of ammonia. Therefore, the rate of the reaction is equal to the rate constant, k.

The rate of the reaction can also be expressed in terms of the change in concentration of the reactant over time:

Rate = -Δ[A]/Δt

where Δ[A] is the change in concentration of the reactant and Δt is the change in time.

Given that the initial amount of ammonia is 350 mmol and the final amount is 175 mmol, the change in concentration of ammonia is:

Δ[A] = 175 mmol - 350 mmol = -175 mmol

The negative sign indicates that the concentration of ammonia is decreasing over time.

Substituting the values into the rate equation gives:

-0.0054 M/s = -175 mmol / Δt

Solving for Δt gives:

Δt = 175 mmol / 0.0054 M/s

However, we need to convert the amount of ammonia from mmol to mol because the rate constant is given in M/s. There are 1000 mmol in 1 mol, so:

Δt = 175 / 1000 mol / 0.0054 M/s

Finally, we need to convert the volume from L to m^3 because the rate constant is given in M/s. There are 1000 L in 1 m^3, so:

Δt = 175 / 1000 mol / (0.0054 M/s * 3 / 1000 m^3)

Solving for Δt gives:

Δt = 10880 s

Therefore, it will take approximately 10880 seconds for the amount of ammonia to decrease from 350 mmol to 175 mmol.

The reaction is zero order in ammonia, which means the rate of the reaction is independent of the concentration of ammonia. The rate equation for a zero order reaction is:

Rate = k

where k is the rate constant.

In this case, the rate constant k is given as 0.0054 M/s.

The rate can also be expressed in terms of the change in concentration over time:

Rate = -d[NH3]/dt

where [NH3] is the concentration of ammonia and t is time.

Setting these two expressions for the rate equal to each other gives:

-d[NH3]/dt = k

Rearranging to solve for time gives:

dt = -d[NH3]/k

Integrating both sides from the initial concentration to the final concentration gives the time it takes for the concentration to change from the initial to the final value:

∫dt = -∫d[NH3]/k

t = -([NH3]final - [NH3]initial)/k

The initial concentration of ammonia is 350 mmol in a 3.0 L flask, or 350 mmol/3.0 L = 116.67 mM.

The final concentration of ammonia is 175 mmol in a 3.0 L flask, or 175 mmol/3.0 L = 58.33 mM.

Substituting these values into the equation for time gives:

t = -((58.33 mM - 116.67 mM) / 0.0054 M/s)

t = 10815.74 s

Rounding to two significant figures gives:

t = 11000 s