Problem 30 - Chemistry for Allied Health

Question

Substance A disappears at a rate of \(0.0250 \mathrm{M} / \mathrm{s}\). If the initial concentration is \(4.00 \mathrm{M}\), what is the concentration after one minute?

Step-by-Step Solution

Answer

The concentration after one minute is 2.50 M.

Step 1: Identify the Given Information

The rate of disappearance of Substance A is given as \(0.0250 \text{ M/s}\). The initial concentration of Substance A is \(4.00 \text{ M}\). We need to find the concentration after one minute.

Step 2: Convert Time into Seconds

One minute is equal to 60 seconds. Therefore, when we are calculating the concentration change over one minute, we need to consider \(60 \text{ seconds}\).

Step 3: Calculate the Change in Concentration

The change in concentration over the given time period can be calculated using the formula: \(\Delta [A] = \text{rate} \times \Delta t\). Substituting the given values: \(\Delta [A] = 0.0250 \text{ M/s} \times 60 \text{ s}\).

Step 4: Perform the Multiplication

Calculate the change in concentration: \(\Delta [A] = 0.0250 \times 60 = 1.50 \text{ M}\). This is the amount by which the concentration decreases.

Step 5: Calculate the Final Concentration

Subtract the change in concentration from the initial concentration to find the final concentration: \([A]_{final} = 4.00 \text{ M} - 1.50 \text{ M} = 2.50 \text{ M}\).

Key Concepts

Concentration Change

Whenever a chemical reaction takes place, the concentration of the reactants decreases, and the concentration of the products increases. This variation in concentration over a certain period is termed as concentration change. In the context of our problem, we want to know how much Substance A's concentration changes over time.
The formula for calculating concentration change (4[A]) is given by:

• c[A] = ext{rate} imes c t

This formula tells us that the change in concentration directly depends on the rate of disappearance and the time for which the change occurs. In our exercise, we applied this formula to determine how much the concentration of Substance A decreases after one minute, given a disappearance rate of 0.0250 M/s.

Initial Concentration

The initial concentration of a substance in a reaction refers to how much of the reactant is present before the reaction starts taking place.
In chemical problems like the one we tackled, knowing the initial concentration is crucial because it acts as a starting point for calculating how much of the substance will remain or be used up after a certain time period.

• In our problem, the initial concentration of Substance A is given as 4.00 M.

From this value, we subtract the change in concentration calculated during the reaction to find out the final concentration at the end of the given time period.

Rate of Disappearance

The rate of disappearance is a measure of how quickly a reactant is being consumed in a reaction.
In other words, it tells us how fast the concentration of a reactant decreases over a specific duration of time. The rate of disappearance is often expressed in units like M/s (molarity per second), as seen in our specific problem.
If we know the rate of disappearance, we can easily compute how much of the reactant will be "used up" over a set amount of time. This concept is key to predicting the outcomes of reactions.

Time Conversion

Chemical reactions generally discuss time in seconds, but often you'll encounter problems where time is given in minutes, hours, or even days.
Converting time to seconds is crucial for calculations where time-related changes are given in per-second terms, like a rate of disappearance in our exercise.

• It's simple to convert: 1 minute equals 60 seconds.
• Having time in the correct units ensures consistency and correct calculations.

For our problem, converting time from minutes to seconds was necessary to compute the concentration change accurately using the given rate of disappearance.