First Order Reaction Kinetics

First order consumption

When consumption rate is proportional to the current concentration, C = C₀ exp(−kt) describes its evolution. Here k is the rate coefficient. Time and coefficient units must agree, so the calculator converts both to a seconds basis. Starting at 2 mol/L with k = 0.01 1/s gives 1 mol/L after 69.3147 seconds.

Target concentration

The time tab accepts a positive target at or below the initial value. An unchanged concentration requires zero time. This equation alone cannot establish that a reaction is first order. Experimental fit, temperature control and constant volume must be assessed separately.

Reading coefficient and time together

The exponent k·t must be dimensionless. Do not directly multiply an inverse second coefficient by a time in minutes. Correct unit selections let the calculator convert them. For an experimental coefficient, compare temperature, substance and medium with your case. It is not a universal reaction constant.

For example, let initial concentration be 4 mol/L, target 1 mol/L and an illustrative experimental coefficient 0.05 1/s. The ratio is 4/1 = 4, so time is ln(4)/0.05 ≈ 27.725887 s. The remaining fraction is 1/4, giving 75 percent conversion. Half life is ln(2)/0.05 ≈ 13.862944 s. Two half lives reach the target because the concentration halves and then the remainder halves again.

Conversion and remaining concentration are different outputs. Changing initial concentration does not change half life in this model, but may change time to an absolute target. Temperature changes, reverse reaction or volume changes may require another model. Complete depletion has no finite target time. A tiny value displayed as zero does not prove complete chemical depletion.

Frequently asked questions

How do you calculate concentration in a first order reaction?

For example, the first order consumption equation gives 0.7358 mol/L after 100 seconds for an initial concentration of 2 mol/L and a rate constant of 0.01 1/s. The calculation assumes constant temperature and volume with valid first order kinetics, and does not establish reaction order experimentally.

Calculate with these values