# 4.5: pH scale for concentration of Acids and Bases

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## The pH Scale

**What is pH?**

The pH scale measures the concentration of hydronium ions in water. In section 3.5 we looked at the autoionization of water, which is when two water molecules collide and one gives a proton to another, resulting in the formation of hydronium and hydroxide ions.

H_{2}O(l) + H_{2}O(l) --> H_{3}O^{+}(aq) + OH^{-}(aq)

For neutral water the hydronium and hydroxide concentrations are equal, and this is a very small number, 10^{-7}M. As these are very small numbers we use a log scale to represent pH, which is a convenient way of expressing the hydronium ion concentration of a solution. It is fairly common knowledge that neutral water has a pH of 7, acids have a pH <7 and bases have a pH>7, but few people understand this in terms of the actual hydronium ion concentration. Our objective is to develop an understanding of logarithmic scales by developing a pH scale. First we will introduce the** convention of using brackets to describe concentration**, so [H_{3}O^{+}] means the concentration of hydronium in moles per liter (M).

**pH = -log[H _{3}O^{+}]**

**[H _{3}O^{+}] = 10^{-pH} = 1/10^{pH}**

So a [H_{3}O^{+}] concentration of 1.0x10^{-7} M solution has a pH of 7.00. Note, in pH the significant Figures are given by the number of places to the left of the decimal, as it is not a number, but the number of times something has been divided (or multiplied) by 10. To understand this, consider a solution with a concentration of 1x10^{-12}, the number has 1 significant Figure and the pH is 12. Since 12 has two digits, we can't use the digits to the left of the decimal, and so we write it as 12.0, indicating it has 1 significant digit.

To get a feel for this we can use the following applet and the method of successive dilutions to develop a pH scale.

## Developing pH Scale via Method of Successive Dilutions

Method of Successive Dilutions:

We have created a demonstration video, which describes the features and interface of the Virtual Lab.

In the virtual lab below:

Part 1: Setting up the lab for the method of successive dilutions.

- Open the stockroom and go to the strong acids
- single click on 1 M HCl,
- single click on the 3 L distilled water

- Click on "glassware" and move into the workbench a 100 mL volumetric flask
- Drag the water over the 100 mL volumetric flask and transfer 90 mL of water into the flask.
- right click on the volumetric flask and hit "duplicate". repeat this 7 times, so you have 8 100 mL flasks with each containing 90 mL of water.
- Click on 1 M HCl, and read the pH, which will be 0, because 1 = 10
^{-pH}= 10^{0}= 1.

Part 2: Successive Dilutions.

- Click on the stock 1 M HCl and record the pH
- Transfer 10 ml of 1 M HCl to a volumetric flask with 90 mL water, so the total volume is 100 mL, and record the pH of the diluted solution, which represents 10 mL osf the stock dilute to 100 mL,
- From the dilution equation, M
_{i}V_{i}= M_{i}V_{i}and

\[M_{f} = M_{i}\left ( \frac{V_{i}}{V_{f}} \right )\] Note, the ratio of the volumes is unit-less and can be defined as the dilution factor, which in this case is 10:100 or 1 to 10, so the diluted solution is 1/10th the original. - If you successively dilute each solution 10 fold by pouring 10 mL into 90 mL of water, the pH of each solution is n, where n is the number of times you successively diluted the stock 1M solution.
- That is, each solution is 1/10
^{n}the concentration of the original solution, where n is the number of times the original solution was successively diluted, and so the pH is the number of 1/10 dilutions.

- From the dilution equation, M

**Why after eight 10-fold dilutions does the pH not become 8, but stays at 7?**

Neutral water is the result of one water molecule transferring a proton to another water molecule, and this results in a hydronium concentration of 10^{-7}. When the acid is diluted to a concentration of less than 10^{-7}, it is so dilute that it protonates fewer water molecules than the water does.

Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to:

- anonymous