The pH of a solution changes from 5.5 to 3.5.
This indicates that the [OH−] of the solution
has
1. increased by a factor of 100.
2. increased by a factor of 2.
3. decreased by a factor of 2.
4. decreased by 2 M.
5. decreased by a factor of 100.
6. increased by 2 M.
5 is the answer.
5.5 to 3.5 the solution has become more acid by pH of 2 and since this is a log term (pH = -log(H^+) that's more acidic by a factor of 100.
So OH must have decreased by a factor of 100.
Oh, pH changes can be quite tricky! But don't worry, I'm here to bring some laughter. The change in pH from 5.5 to 3.5 indicates that the solution has become more acidic. Now, let's figure out what happened to the [OH-]. Since the solution became more acidic, we can conclude that the [OH-] has decreased. But how much did it decrease? Well, if we compare the pH values, we can see that the difference is 2. So, the [OH-] has decreased by a factor of 100. So, the answer is 5. Decreased by a factor of 100. Keep those pH levels in check, my friend!
The pH scale is a logarithmic scale that measures the acidity or basicity of a solution. A decrease in pH indicates an increase in acidity, while an increase in pH indicates a decrease in acidity.
To determine how the [OH-] of the solution has changed, we need to consider the relationship between the pH and the [OH-] concentration. In an aqueous solution, the concentration of [OH-] and [H+] are related by the equation:
pH = -log[H+]
Since pH is based on the logarithm, a change in pH by 1 unit represents a tenfold change in [H+]. In other words, if the pH decreases by 1 unit, the [H+] concentration increases by a factor of 10.
In this case, the pH of the solution decreases from 5.5 to 3.5, which means the acidity has increased. To determine how the [OH-] has changed, we need to consider that:
pOH = -log[OH-]
Since the sum of pH and pOH is always 14 at 25°C, we can calculate the pOH of the initial solution:
pH + pOH = 14
5.5 + pOH = 14
pOH = 8.5
From the equation above, we can calculate that the [OH-] concentration in the initial solution is 10^(-8.5) M.
Similarly, we can calculate the pOH of the final solution:
pH + pOH = 14
3.5 + pOH = 14
pOH = 10.5
From the equation above, we can calculate that the [OH-] concentration in the final solution is 10^(-10.5) M.
Now, let's compare the initial and final [OH-] concentrations:
[OH-]initial = 10^(-8.5) M
[OH-]final = 10^(-10.5) M
To determine the factor by which the [OH-] has changed, we divide the final concentration by the initial concentration:
[OH-]final / [OH-]initial = (10^(-10.5) M) / (10^(-8.5) M) = 10^(-10.5+8.5) = 10^(-2)
Therefore, the [OH-] of the solution has decreased by a factor of 100. So the correct option is 5. decreased by a factor of 100.
To determine the change in the [OH−] concentration of a solution based on a change in pH, we need to understand the relationship between pH and [OH−] concentration.
The pH is a measure of the acidity or alkalinity of a solution and is determined by the concentration of hydrogen ions ([H+]). Mathematically, pH is defined as the negative logarithm (base 10) of [H+]. Therefore, a decrease in pH corresponds to an increase in [H+] concentration, indicating a more acidic solution.
On the other hand, the [OH−] concentration is related to the [H+] concentration through the equation: [H+] × [OH−] = 1.0 × 10^(-14) M² at 25°C. As a result, when [H+] increases, the [OH−] concentration decreases, and vice versa.
In this case, the solution's pH decreases from 5.5 to 3.5. This indicates that the [H+] concentration has increased. Remember that a decrease in pH means an increase in [H+]. Therefore, the [OH−] concentration must have decreased. Now let's eliminate the incorrect options based on this information.
Option 1: The [OH−] concentration has "increased by a factor of 100." This is incorrect based on our previous explanation. The [OH−] concentration actually decreases when the pH decreases.
Option 2: The [OH−] concentration has "increased by a factor of 2." This is also incorrect because, as mentioned, the [OH−] concentration decreases when the pH decreases.
Option 4: The [OH−] concentration has "decreased by 2 M." This is incorrect because the [OH−] concentration is not given as a specific value, but rather in terms of a factor.
Option 6: The [OH−] concentration has "increased by 2 M." This is incorrect because we established that the [OH−] concentration decreases when the pH decreases.
This leaves us with two remaining options:
3. The [OH−] concentration has "decreased by a factor of 2."
5. The [OH−] concentration has "decreased by a factor of 100."
Since the pH has decreased by 2 units, which is a factor of 100 (10²) in terms of concentration, we can conclude that option 5 is the correct answer. Therefore, the [OH−] concentration of the solution has decreased by a factor of 100.