A solution with a pH of 2.0 has a hydronium ion concentration ten times greater than a solution with a pH of?
A solution with a pH of -8.0! That's right, it's so acidic that it's off the charts, literally. It's like the Grumpy Cat of solutions - nobody wants to be around it! But hey, at least the hydronium ions are having a wild party in there.
The pH scale is a logarithmic scale used to measure the acidity or alkalinity of a solution. It measures the concentration of hydronium ions (H3O+) in a solution. The formula to calculate pH is:
pH = -log[H3O+]
To determine the pH of a solution that has a hydronium ion concentration ten times greater than a solution with a pH of 2.0, we can use the fact that the pH scale is logarithmic.
Let's start by calculating the hydronium ion concentration of the solution with a pH of 2.0. Using the formula:
pH = -log[H3O+]
Rearranging the formula:
[H3O+] = 10^(-pH)
Substituting the value of pH = 2.0:
[H3O+] = 10^(-2.0)
[H3O+] = 0.01 mol/L
Now, we need to find the solution with a hydronium ion concentration ten times greater. We can do this by multiplying the concentration of the first solution (0.01 mol/L) by 10:
New [H3O+] = 0.01 mol/L * 10 = 0.1 mol/L
To determine the pH of the new solution, we can use the same formula:
pH = -log[H3O+]
Substituting the value of [H3O+] = 0.1 mol/L:
pH = -log(0.1)
Using logarithmic properties:
pH ≈ -log(10^(-1))
pH ≈ -(-1)
pH ≈ 1.0
Therefore, the solution with a hydronium ion concentration ten times greater than a solution with a pH of 2.0 has a pH of approximately 1.0.
To find the pH of a solution with a hydronium ion concentration ten times lower, we can use the equation:
pH = -log[H3O+]
Since the given solution has a pH of 2.0, we can find the hydronium ion concentration by converting the pH value to a decimal:
[H3O+] = 10^(-pH)
[H3O+] = 10^(-2.0)
[H3O+] = 0.01 M
Since we want to find the hydronium ion concentration ten times lower, we divide the current concentration by 10:
[H3O+]_new = [H3O+] / 10
[H3O+]_new = 0.01 M / 10
[H3O+]_new = 0.001 M
Now, to find the pH of the new solution, we can use the equation:
pH_new = -log[H3O+]_new
pH_new = -log(0.001)
Using a calculator, we can solve for the pH_new:
pH_new ≈ 3.0
Therefore, a solution with a pH of 2.0 has a hydronium ion concentration ten times greater than a solution with a pH of 3.0.