Calculate the pH and pOH of aqueous solutions with the...

Calculate the pH and pOH of aqueous solutions with the following concentrations at 298 $\mathrm{K}$ . a. $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-6} M$ b. $\left[\mathrm{OH}^{-}\right]=6.5 \times 10^{-4} M$ c. $\left[\mathrm{H}^{+}\right]=3.6 \times 10^{-9} M$ d. $\left[\mathrm{H}^{+}\right]=2.5 \times 10^{-2} \mathrm{M}$

Calculate the pH and pOH of aqueous solutions with the following concentrations at 298 $\mathrm{K}$ .
a. $\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-6} M$
b. $\left[\mathrm{OH}^{-}\right]=6.5 \times 10^{-4} M$
c. $\left[\mathrm{H}^{+}\right]=3.6 \times 10^{-9} M$
d. $\left[\mathrm{H}^{+}\right]=2.5 \times 10^{-2} \mathrm{M}$

Key Concepts

pH and pOH

pH and pOH are measures of the acidity and basicity of a solution, respectively. pH is defined as the negative logarithm of the hydrogen ion concentration, while pOH is the negative logarithm of the hydroxide ion concentration. At 298 K, they are related by the equation pH + pOH = 14, which allows one to calculate one if the other is known.

Water Auto-Ionization (Kw)

Water auto-ionization refers to the self-ionization of water into hydrogen ions (H?) and hydroxide ions (OH?) at equilibrium. The equilibrium constant for this process, denoted as Kw, is approximately 1.0 x 10?¹? at 298 K. This constant is critical for calculating pH and pOH in aqueous solutions since it links the concentrations of H? and OH? ions.

Logarithmic Calculations in Chemistry

Logarithmic functions, particularly the negative logarithm, are used to convert very small ionic concentrations into a more manageable scale for pH and pOH. This transformation simplifies the wide range of ion concentrations encountered in chemical solutions and provides an intuitive understanding of the solution's acidity or basicity.

Concentration Measurements

Concentration measurements, such as molarity, indicate the number of moles of solute per liter of solution and are essential for calculating pH and pOH. Accurate measurement of ion concentrations (H? or OH?) is fundamental for applying the definitions of pH and pOH, and for utilizing the water auto-ionization constant in these calculations.

Transcript

00:02 There, in this question for each of these solutions, we are trying to determine both the ph and the poh.

00:13 Well, we can calculate ph if we know the h plus concentration, because ph is equal to the negative log of the h plus concentration.

00:27 We can calculate poh if we know the hydroxide ion concentration, concentration, because that is equal to the negative log of the hydroxide ion concentration.

00:41 All right, so for each of these, we're given the concentration of either the oh minus or the h plus.

00:47 So we can find ph or poh for each one that way.

00:50 So for example, for letter a, since we're given the oh minus concentration, we can calculate the poh by taking the negative log of one point 0 times 10 to the negative 6.

01:10 That's going to give us a p -o -h, and we take the log of that and reverse the sign, of 6.

01:16 And it needs to be written as 6 .00 because for significant figures, since there are two significant figures in our number, when we take the log of that, we need two decimal places.

01:27 That's how significant figures work with logs.

01:32 All right, but then we need the p -h.

01:34 Well, well, there are a couple ways we can get the ph.

01:36 One is we could calculate the h plus concentration first.

01:41 Or more simply, what we could do is use the equation that tells us that at 25 degrees celsius, ph plus poh is going to add up to 14 for any aqueous solution at 25 degrees celsius, which is where we're at at 298 kelvin.

02:02 All right, so if poh is 6 .00, we subtract that from 14, and we get a ph of 8 .00.

02:09 All right, moving on, letter b again gives us the oh minus concentration.

02:15 So when we take the log of 6 .5 times 10 to the negative fourth, that gives us the poh...

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