Question

much of the sulfur used in the united states comes from the hydrogen sulfide contaminant that makes \sour\ natural gas smell bad. hydrogen sulfide is separated from the other components of natural gas mostly by taking advantage of its acid - base reaction with aqueous ethanolamine:
ho(ch₂)₂nh₂(aq)+h₂s(g)→ho(ch₂)₂nh₃⁺(aq)+hs⁻(aq)
suppose an engineer decides to study the rate of this reaction. he prepares four reaction vessels with 179.9 ml of ethanolamine solution and 14.7 g of hydrogen sulfide gas each. the volume and temperature of each vessel is shown in the table below.
arrange the reaction vessels in decreasing order of initial rate of reaction. in other words, select a \1\ next to the vessel in which the engineer can reasonably expect the initial rate of reaction to be highest, a \2\ next to the vessel in which the initial rate of reaction would be next highest, and so on.

Explanation:

Step1: Analyze the effect of temperature on reaction rate

According to the Arrhenius equation \(k = A e^{-E_a/(RT)}\), the rate constant \(k\) increases with increasing temperature \(T\). Higher temperature provides more kinetic energy to reactant molecules, increasing the frequency of effective collisions.

Step2: Compare the temperatures of different vessels

Vessel \(C\) has the highest temperature (\(38.^{\circ}C\)), vessel \(B\) and \(D\) have the same temperature (\(37.^{\circ}C\)), and vessel \(A\) has the lowest temperature (\(35.^{\circ}C\)).

Step3: Analyze the effect of volume on reaction rate (considering concentration, assuming amount of reactants is the same)

The rate of a reaction (for a given reaction mechanism) is related to the concentration of reactants (for example, for a reaction \(aA + bB
ightarrow cC + dD\), rate \(r=k[A]^m[B]^n\)). If the amount of reactants is fixed, a smaller volume leads to a higher concentration. Vessels \(B\) and \(C\) have a smaller volume (\(2.0L\)) compared to vessels \(A\) and \(D\) (\(4.0L\)).

Step4: Rank the initial rates

Since vessel \(C\) has the highest temperature and a relatively small volume (higher concentration compared to \(A\) and \(D\)), its initial rate is the highest. Then, between \(B\) and \(D\) (same temperature), \(B\) has a smaller volume (higher concentration if amount of reactants is fixed), so \(B\) has a higher rate than \(D\). Vessel \(A\) has the lowest temperature and a large volume (lowest concentration if amount of reactants is fixed), so it has the lowest rate.

Answer:

\(C > B> D > A\)