Question 2
The pH of a substance is a measure of its acidity and is given by the formula $\text{pH}=-\log_{10}[\text{H}^+]$ where $[\text{H}^+]$ is the concentration of hydrogen ions in moles per litre. If a solution has a pH equal to 0.2, the concentration of hydrogen ions in moles per litre is closest to
Not quite. Check it in the formula: $-\log_{10}(0.32)\approx0.49$, not 0.2. Rewrite the equation in index form to undo the log.
That’s it. Step through the hints below to see why.
Not quite. 0.70 is $-\log_{10}(0.2)$. That treats 0.2 as the concentration. Here 0.2 is the pH, so you need to undo the log, not take it.
Close, but the sign is off. 1.58 is $10^{0.2}$, and $-\log_{10}(1.58)\approx-0.2$. Move the minus first: $\log_{10}[\text{H}^+]=-0.2$, so $[\text{H}^+]=10^{-0.2}$.
This is the solution. At $[\text{H}^+]=10^{-0.2}\approx0.63$ the pH is exactly 0.2, so the point sits on the blue line.
Very close. The point looks as if it sits on the blue line, but the pH here is , not exactly 0.2. Use the button below for the exact concentration.
The pH here is , more than 0.2. A higher pH means fewer hydrogen ions, so the concentration you want is bigger than this. Move right.
The pH here is , less than 0.2. A lower pH means more hydrogen ions, so the concentration you want is smaller than this. Move left.
Put the pH you know into the formula.
$$0.2=-\log_{10}[\text{H}^+]$$
The unknown is the concentration, inside the log.
Move the minus sign across first, then rewrite the log in index form.
$$\log_{10}[\text{H}^+]=-0.2$$
$$[\text{H}^+]=10^{-0.2}$$
Evaluate with your calculator.
$$10^{-0.2}\approx0.631$$
Check by substituting back: $-\log_{10}(0.631)\approx0.2$. A pH a little above 0 means a concentration a little below 1, so 0.63 makes sense.
$$-\log_{10}[\text{H}^+]=0.2$$
$$\log_{10}[\text{H}^+]=-0.2$$
$$[\text{H}^+]=10^{-0.2}\approx0.63$$
The concentration is about 0.63 moles per litre.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2020 QCAA Mathematical Methods external assessment, © State of Queensland (QCAA) 2020, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
Spot a mistake on this page? Report it