Question

when carbon dioxide gas dissolves in water, it reacts with the water to form carbonic acid. this is why soft drinks have a low ph, and soda water is often recommended as a mild cleaning agent. it is also why there is concern that rising levels of atmospheric carbon dioxide may cause the earths oceans to become more acidic. here is the reaction between carbon dioxide gas and water:
h₂o(l)+co₂(g)→h₂co₃(aq)
suppose an engineer decides to study the rate of this reaction. she prepares four reaction vessels with 127.0 g of water and 20.5 g of carbon dioxide 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 collision theory, the higher the temperature, the more kinetic energy molecules have. Molecules with higher kinetic energy are more likely to collide with sufficient energy (activation energy) to react. So, higher temperature generally leads to a higher reaction rate.

Step2: Analyze the effect of concentration on reaction rate

The concentration of reactants can be calculated using \(n = \frac{m}{M}\) (where \(m\) is mass and \(M\) is molar mass. For \(CO_2\), \(M = 44\space g/mol\), for \(H_2O\), \(M = 18\space g/mol\)). The number of moles of \(CO_2\): \(n_{CO_2}=\frac{20.5\space g}{44\space g/mol}\approx0.466\space mol\). The number of moles of \(H_2O\): \(n_{H_2O}=\frac{127.0\space g}{18\space g/mol}\approx7.06\space mol\). The concentration \(c=\frac{n}{V}\).

• Vessel A: \(c_{CO_2}^A=\frac{0.466\space mol}{4.0\space L}\approx0.117\space mol/L\)
• Vessel B: \(c_{CO_2}^B=\frac{0.466\space mol}{2.0\space L}= 0.233\space mol/L\)
• Vessel C: \(c_{CO_2}^C=\frac{0.466\space mol}{4.0\space L}\approx0.117\space mol/L\)
• Vessel D: \(c_{CO_2}^D=\frac{0.466\space mol}{2.0\space L}= 0.233\space mol/L\)

Combining the effect of temperature and concentration:

• Vessel D has a higher temperature (\(41^{\circ}C\)) than vessel B (\(40^{\circ}C\)) and the same \(CO_2\) concentration as vessel B. Higher temperature in vessel D means higher reaction rate than vessel B.
• Vessel B has higher \(CO_2\) concentration than vessel A (same temperature range, \(40^{\circ}C\) vs \(39^{\circ}C\), small temperature difference, concentration effect is more significant here as \(CO_2\) is the limiting reactant in terms of concentration change). Vessel C has lower \(CO_2\) concentration than vessel D (higher temperature in D) and lower temperature than D.

Answer:

D > B > C > A