A student wants to determine how long it takes to dissolve 51.3 g of common table salt (sodium chloride) in 1L of water by monitoring the solution. It takes 26.7 seconds for the salt to completely dissolve. Determine the rate of dissolution. Find the rate constant expression if the reaction was first-order for NaCl.
How do I solve this problem?
To solve this problem, you need to determine the rate of dissolution and the rate constant expression for the reaction.
1. Start by calculating the rate of dissolution. The rate of dissolution is usually defined as the change in concentration of the substance per unit time. In this case, it can be calculated by dividing the amount of salt dissolved by the time it took to dissolve:
Rate of dissolution = Amount of salt dissolved / Time taken to dissolve
You're given that 51.3 g of salt dissolved in 26.7 seconds, so the rate of dissolution would be:
Rate of dissolution = 51.3 g / 26.7 s
2. Simplify the calculation for the rate of dissolution:
Rate of dissolution ≈ 1.919 g/s
3. Now, to determine the rate constant expression, you need to know the order of the reaction with respect to sodium chloride (NaCl). The given problem states that the reaction is first-order for NaCl.
In a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. Mathematically, it can be expressed as:
Rate = k [A]
Where:
- Rate is the rate of reaction,
- k is the rate constant, and
- [A] is the concentration of the reactant.
In this case, the reactant is NaCl, so the rate constant expression would be:
Rate = k [NaCl]
4. Since the rate of dissolution can be expressed as the change in concentration of NaCl over time, you can rewrite the rate constant expression in terms of the rate of dissolution:
Rate of dissolution = k [NaCl]
Now, substitute the calculated rate of dissolution value:
1.919 g/s = k [NaCl]
Note that the units of the rate constant will depend on the units used for the rate of dissolution and concentration.
Therefore, the rate constant expression for the first-order reaction of NaCl is 1.919 g/s = k [NaCl].