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Hplus Calculator + Online Solver With Free Steps

The Hplus Calculator finds the total Hydrogen (H+) or Hydroxide (OH-) concentration in a solution given its pH or pOH.

You can only find one ion’s concentration from one of the pH or pOH. If you choose pH, the calculator will output the hydrogen ion concentration. If you select pOH instead, you will get the hydroxide ion concentration.

This limitation is inherent to the fact that not all solutions maintain the assumption that pH + pOH = 14 (at room temperature ONLY). Therefore, you cannot generally get both ions’ concentrations from just one of the pH or pOH at any given temperature. 

If, however, you know the self-ionization product of water at that temperature, then pH + pOH = pKw, where pKw is the self-ionization product of water at a particular temperature. 

What Is the Hplus Calculator?

The Hplus Calculator is an online tool that calculates a solution’s hydrogen or hydroxide ion concentrations from its pH or pOH value. The calculator can only find H+ concentration if you provide the pH and the OH- when you provide the pOH.

The calculator interface consists of one drop-down menu and one input text box. The drop-down menu offers a selection between pH and pOH. Once you have selected one of these, you can enter its value into the text box. 

For example, if we wanted to enter a pOH of 3, we would select pOH from the drop-down menu and then enter “3” without quotes into the text box.

How To Use the Hplus Calculator?

You can use the Hplus Calculator to the concentration of hydrogen or hydroxide ions in a solution given its pH or pOH value.

For example, suppose you want to find the hydrogen ion concentration in a solution whose measured pH is 9. You can use the calculator to do this by following the step-by-step guidelines below.

Step 1

Select either pH or pOH from the drop-down menu. For our mock example, you would select pH here.

Step 2

Enter the value of pH or pOH in the text box next to it. Enter “9” without quotes here for the mock example.

Step 3

Press the Submit button to get the results.

Results

The results show up in a new window that contains three sections. The first one is labeled “Input Information.” It shows the calculator’s input interpretation, which you can use for verification.

The second section is labeled “Result” and displays the actual hydrogen or hydroxide ion concentrations. It presents them in various units, and you can choose to view just a few or all seven units using the prompt “More Units/Fewer Units” at the top-right corner of this section.

The final section is labeled “Equation” and contains the base equation used in the calculations. We describe these equations under the next heading.

For the mock example, the results are as follows:

  • Input Information

pH
pH9
  • Result

Hydrogen ion concentration

1 nmol/L (nanomole/liter)

= 1 nM (nanomolar)

= 1000 (picomolar)

  • Equation

pH = -log([H+])
[H+]Hydrogen ion concentration
pHpH

 

How Does the Hplus Calculator Work?

The Hplus Calculator works by using the following formulae:

[H+] = 10$^\boldsymbol{\textsf{-pH}}$

[OH-] = 10$^\boldsymbol{\textsf{-pOH}}$

What are pH and pOH?

The pH scale is a logarithmic scale used to measure the acidity or alkalinity of a solution. The values range from 0 (extremely acidic) to 14 (extremely alkaline). The pH value of a solution is a number on this scale that indicates how acidic or alkaline a given solution is. 

Intuitively, pH is a measure of hydrogen ion concentration in a solution. The lower the pH, the larger the presence of this ion relative to hydroxide ions. Thus, high hydrogen ion concentration means the solution is likely acidic.

Pure water has a pH of 7 (completely neutral). Sulfuric acid at 33.5% concentration has a pH of 0.5, which is highly corrosive and acidic. Sodium Hydroxide is an example of a strong alkali with a pH of 14.

The pOH scale is the opposite of pH and measures the hydroxide ion concentration in a solution. At room temperature, pH and pOH are related by: 

pH + pOH = 14

At non-room temperatures, the equation is different:

 pH + pOH = pKw

Here, pKw is the self-ionization product of water. It is a constant for a fixed temperature, but its value changes at different temperatures. Therefore, just knowing the pH is not enough to get both the H+ and OH- concentrations; we also need the value of pKw at the solution’s temperature.

Derivation

The above equations are results of the fact that:

pH = -log([H+])

pOH = -log([OH-])

Where [H+] represents the hydrogen ion concentration and [OH-] shows the hydroxide ion concentration within the solution (default units: moles/liter or mol/L). From this, we can proceed as follows:

-pH = log([H+])

-pOH = log([OH-])

Since the logarithm is to the base 10 and we know that if log$_\textsf{b}$(x) = y with b being the base, then b$^\mathsf{y}$ = x. Therefore, with base 10, we get:

[H+] = 10$^\textsf{-pH}$

[OH-] = 10$^\textsf{-pOH}$

We can see that the pH is inversely related to the hydrogen ion concentration. Thus, the greater the pH, the smaller the hydrogen ion concentration. The same applies to pOH and the hydroxide ion concentration.

Solved Examples

Example 1

Find the hydrogen ion concentration of a solution with a known pH value of 4.32. The desired concentration unit is micromoles per cubic meter.

Solution

Since we know that [H+] = 10$^\textsf{-pH}$, we get the following result:

[H+] = 10$^\mathsf{-4.32}$

[H+] = 4.7863 x 10$^\mathsf{-5}$ moles/liter = 47.863 x 10$^\mathsf{-6}$ moles/liter

Since one micromole = 1 x 10$^\mathsf{-6}$ mole, we have:

[H+] = 47.863 micromoles/liter

By definition, one liter = one cubic decimeter. Since 1 meter = 10 decimeters, 1 cubic meter = 10$^\mathsf{3}$ cubic decimeters = 1000 cubic decimeters.

Therefore, 1 cubic meter = 1000 liters and 1 liter = 0.001 cubic meters:

[H+] = (47.863 / 0.001) micromoles/cubic meter

[H+] = 47863 micromoles/cubic meter

[H+] = 47863 $\boldsymbol\mu$mol/m$^\boldsymbol{\mathsf{3}}$

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