Question

A flask is charged with 0.100 mol of A and allowed to react to form $B$ according to the hypothetical gas-phase reaction $A(g)⟶\mathrm{B}(g).$ The following data are collected:(a) Calculate the number of moles of $\mathrm{B}$ at each time in the table, assuming that $\mathrm{A}$ is cleanly converted to $\mathrm{B}$ with no intermediates. (b) Calculate the average rate of disappearance of A for each 40 s interval in units of mol/s. (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A?

Short answer

To calculate the number of moles of B at each time, use the equation n(B) = 0.100 - n(A). For each time interval, calculate the average rate of disappearance of A by dividing the change in moles of A by 40 seconds. To express the rate in units of concentration per time, the volume of the reaction flask is needed.

Step-by-step solution

Calculate the number of moles of B at each time

To calculate the number of moles of B at each time, we just need to track the disappearance of A, assuming that A is cleanly converted to B with no intermediates. Let's denote the moles of A left at a certain time as n(A). Since we start with 0.100 mol of A, the moles of B formed at that time is: n(B) = 0.100 - n(A) Therefore, for each time, we just need to subtract the moles of A left from 0.100 to find the moles of B formed.

Calculate the average rate of disappearance of A

To find the average rate of disappearance of A for each interval, we need to find the change in moles of A during the 40-second intervals and divide by the interval length. Let's denote the initial moles of A of an interval as n(A1) and the final moles of A of the same interval as n(A2). Then the average rate of disappearance of A in that interval in units of mol/s is: Average rate = (n(A1) - n(A2)) / 40 Calculate this average rate for each 40 s interval given in the table.

Identify the parameters needed for rate in units of concentration per time

We want to find out which of the following parameters is needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A. Since the rate is expressed in concentration per time (i.e. mol/L/s or M/s), we need to convert moles to concentration by dividing with the volume of the reaction flask. Therefore, we need parameter (ii) - the volume of the reaction flask. The pressure of the gas, temperature, and molecular weight of A are not necessary for expressing the rate in units of concentration per time since they are not involved in the relationship between moles and concentration.

Key concepts

Reaction Rates

Understanding reaction rates is crucial for studying the speed at which reactants transform into products in a chemical process. It is quite like measuring how quickly a car travels, except, in this case, we measure the rate at which a reactant disappears or a product forms.

For example, let's consider a reaction where component A is converting to B over time. The reaction rate can be calculated by observing the change in concentration of A or B over a specific time interval. A faster reaction rate implies a greater amount of reactant being converted in a shorter span, signaling a rapidly proceeding reaction.

Concentration

Concentration, often measured in moles per liter (Molarity), is a way of expressing how much of a substance is present in a given volume of solution. It plays a pivotal role in reaction rates. Generally, a higher concentration of reactants leads to an increased number of collisions among particles, which can raise the reaction rate.

In our example with reactant A and product B, knowing the concentration of A can help us understand how quickly the reaction is approaching completion. If the text references the loss of A, we deduce how much B is formed by understanding that concentration is essentially 'how much' in 'how much space'.

Gas-phase Reactions

Gas-phase reactions involve reactants and products in the gaseous state, and their kinetics can be unique compared to those in other phases. The rate of a gas-phase reaction can be influenced by factors such as temperature, pressure, volume, and the presence of a catalyst.

In our exercise, as reactant A turns into product B, both in the gas phase, the rate at which A disappears can be affected by changes in these conditions. However, to simplify, we might assume constant temperature and pressure, keeping our focus on moles and volume to determine the rate.

Rate of Disappearance

The rate of disappearance, as it suggests, describes the rate at which a reactant is used up in a reaction. It's always a positive value, even though the reactant amount is decreasing. The rate of disappearance corresponds to a negative change in the concentration of the reactant over time, with the common units of mol/L/s or M/s.

In step 2 of our provided solution, calculating the average rate of disappearance involves determining the amount of A that has vanished over each time segment. This provides insight into the dynamics of the reaction at various points in time. Getting a grasp on this rate is fundamental for predicting when the reactants will be entirely consumed, which is essential for practical applications such as chemical manufacturing.