In chemistry, the concentration of hydrogen ions in a...

In chemistry, the concentration of hydrogen ions in a solution may be expressed on a pH scale. The equation relating the hydrogen ion concentration $\mathrm{H}^{+}$to the pH of the solution is $\mathrm{pH}=-\log \mathrm{H}^{+}$, where $\mathrm{H}^{+}$is expressed in gram-ions per liter. Thus, a solution which has $10^{-6} \mathrm{~g}$-ion per liter has a $\mathrm{pH}=6$. Conversely, if the given pH of a solution is 8 , then the hydrogen ion concentration is $10^{-8} \mathrm{~g}$-ion per liter. (a) What is the pH of a solution which has a concentration of $10^{-3} \mathrm{~g}$-ion per liter? (b) What is the pH of a solution which has a concentration of 0.004 g -ion per liter? (Hint: Add the positive mantissa and the negative characteristic. Change the sign of the sum.) (c) What is the hydrogen ion concentration of a solution whose pH is 12 ? (d) What is the hydrogen ion concentration of a solution whose pH is 8.4 ? (Hins: Find the antilog of -8.4. Remember that the mantissa must be positive.)

In chemistry, the concentration of hydrogen ions in a solution may be expressed on a pH scale. The equation relating the hydrogen ion concentration $\mathrm{H}^{+}$to the pH of the solution is $\mathrm{pH}=-\log \mathrm{H}^{+}$, where $\mathrm{H}^{+}$is expressed in gram-ions per liter. Thus, a solution which has $10^{-6} \mathrm{~g}$-ion per liter has a $\mathrm{pH}=6$. Conversely, if the given pH of a solution is 8 , then the hydrogen ion concentration is $10^{-8} \mathrm{~g}$-ion per liter.
(a) What is the pH of a solution which has a concentration of $10^{-3} \mathrm{~g}$-ion per liter?
(b) What is the pH of a solution which has a concentration of 0.004 g -ion per liter? (Hint: Add the positive mantissa and the negative characteristic. Change the sign of the sum.)
(c) What is the hydrogen ion concentration of a solution whose pH is 12 ?
(d) What is the hydrogen ion concentration of a solution whose pH is 8.4 ? (Hins: Find the antilog of -8.4. Remember that the mantissa must be positive.)

Key Concepts

Scientific Notation

Scientific notation is a method of writing very large or very small numbers in a compact form, which is especially useful when dealing with the extremely high or low concentrations typical in pH calculations. It expresses numbers as a product of a coefficient and a power of ten, facilitating easier computation and comparison.

Antilogarithms

Antilogarithms, or the inverse logarithmic function, are used to convert a pH value back into a hydrogen ion concentration. This inverse process is critical for determining the actual concentration of hydrogen ions when a pH value is given.

Logarithms

Logarithms convert multiplicative relationships into additive ones, simplifying the handling of quantities that range over several orders of magnitude. In the context of pH, taking the logarithm of the hydrogen ion concentration makes it easier to compare and calculate differences in acidity between solutions.

pH Scale

The pH scale is a logarithmic scale used in chemistry to quantify the acidity or basicity of a solution. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration, which allows a wide range of concentrations to be represented in a more compact numerical format.

Transcript

00:01 Okay, so we're given that the ph of a solution is determined by the formula minus log base 10 of the concentration of hydrogen atoms or hydrogen ions.

00:19 So you're given a bunch of questions that you want to answer about this.

00:27 And so the first one is what is ph when the concentration of hydrogen is 0 .1.

00:43 So in this case, we're just finding ph.

00:47 We know it's the negative log base 10 of this hydrogen concentration, which is negative 0 .1.

00:57 And we know that log base 10 of this number is just, if we go ahead and convert this to 10 to minus 1, we'll see that this is negative negative 1, and then ph is just positive 1.

01:13 And so the second question is the same sort of question, asking what ph when h plus concentration is 0 .001, which we know this is 10 minus 2.

01:26 Similarly to before, we'll see that ph is just a negative log base 10 of 10 to minus 2.

01:35 So we have negative negative 2 or just positive 2.

01:40 And the third question is, what is ph when hydrogen concentration is 0 .001, which is just 10 to the minus 3.

01:54 And we should see as before, this is ph of positive 3.

02:00 So we have 1 and 2 and 3 for abc.

02:05 And then d, we want to talk about what happens to ph as hydrogen ion concentration decreases.

02:14 So we have h plus going down.

02:20 So we know that ph is our formula negative log base 10 of hydrogen at a concentration.

02:30 And so we'll think about what happens to log base 10 as this goes down.

02:38 So as hydrogen concentration goes down, we know that log base 10 must go negative.

02:49 So we can go ahead and graph log base 10 and it's this curve here...

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