A lake receives 8 m3/s of inflow containing 0.3 mol/m3 of a chemical. The chemical reacts with a first order rate constant of 0.01 h-1. The outflow from the lake is also 8 m3/s. Assume there was no chemical in the lake at the beginning and volume of the lake is 106 m3. What will be the concentration changing rate of this chemical in this lake assuming the concentration of such chemical at certain time is X mol/m3 in the lake.

Question

A lake receives 8 m3/s of inflow containing 0.3 mol/m3 of a chemical. The chemical reacts with a first order rate constant of 0.01 h-1. The outflow from the lake is also 8 m3/s. Assume there was no chemical in the lake at the beginning and volume of the lake is 106 m3. What will be the concentration changing rate of this chemical in this lake assuming the concentration of such chemical at certain time is X mol/m3 in the lake.

Answer 1

A lake receives 8 m3/s of inflow containing 0.3 mol/m3 of a chemical. The chemical reacts with a first order rate constant of 0.01 h-1. The outflow from the lake is also 8 m3/s. Assume there was no chemical in the lake at the beginning and volume of the lake is 106 m3. What will be the concentration changing rate of this chemical in this lake assuming the concentration of such chemical at certain time is X mol/m3 in the lake.

Answer 2

To find the concentration changing rate of the chemical in the lake, we need to determine the net change in the chemical concentration per unit time.

In this case, the lake receives an inflow of 8 m3/s with a concentration of 0.3 mol/m3. This means that the rate of chemical entering the lake is given by:

Chemical inflow rate = Inflow volume rate * Inflow concentration = 8 m3/s * 0.3 mol/m3

The outflow from the lake is also 8 m3/s, meaning that the rate of chemical leaving the lake is given by:

Chemical outflow rate = Outflow volume rate * X mol/m3 = 8 m3/s * X mol/m3

Now, let's consider the reaction occurring within the lake. The chemical reacts with a first-order rate constant of 0.01 h-1. This means that the rate of change of the chemical concentration due to the reaction is given by:

Rate of chemical reaction = -k * X mol/m3

Putting it all together, the net change in the chemical concentration per unit time can be calculated as:

Net change rate = Chemical inflow rate - Chemical outflow rate + Rate of chemical reaction
= (8 m3/s * 0.3 mol/m3) - (8 m3/s * X mol/m3) - (0.01 h-1 * X mol/m3)

Since the units of inflow and outflow rates are in m3/s, it is important to note that the units of time for the reaction rate constant (0.01 h-1) need to be converted to match (mol/m3/s).

Now, you can simplify the expression and obtain the concentration changing rate of the chemical in the lake.