Question 7

Some students design an experiment to investigate the effect of hydrochloric acid ( $H C l$ ) concentration on the rate of reaction with calcium carbonate. The apparatus collected carbon dioxide gas in a gas syringe.

Method:

Use a stock solution of $dm−32.5\text{ mol dm}^{-3}$ hydrochloric acid to make a dilution series, including $dm−31.5\text{ mol dm}^{-3}$ and $dm−30.5\text{ mol dm}^{-3}$ acid.
Set up a conical flask containing a fixed mass of calcium carbonate (in excess) and add $cm325\text{ cm}^3$ of the acid solution.
Record the volume of carbon dioxide gas collected in the syringe every $s15\text{ s}$ for $min1\text{ min}$ .
Repeat the experiment three times for each concentration.

Some of the results are shown in the tables below:

Table 1: Results for $dm−30.5\text{ mol dm}^{-3}$ HCl

Time (s)	Trial 1 ( $cm3\text{cm}^3$ )	Trial 2 ( $cm3\text{cm}^3$ )	Trial 3 ( $cm3\text{cm}^3$ )	Mean ( $cm3\text{cm}^3$ )	Standard deviation
15	8	9	8	8.3	0.6
30	15	17	16	16.0	1.0
45	22	24	23	23.0	1.0
60	29	31	30	30.0	1.0

Table 2: Results for $dm−32.5\text{ mol dm}^{-3}$ HCl

Time (s)	Trial 1 ( $cm3\text{cm}^3$ )	Trial 2 ( $cm3\text{cm}^3$ )	Trial 3 ( $cm3\text{cm}^3$ )	Mean ( $cm3\text{cm}^3$ )	Standard deviation
15	25	22	25	24.0	1.7
30	45	41	46	44.0	[ To be calculated ]
45	58	54	56	56.0	2.0
60	67	61	64	64.0	3.0

(i) State the independent variable in this investigation.

(ii) Describe how a student could produce a $dm−31.5\text{ mol dm}^{-3}$ dilute hydrochloric acid solution from the $dm−32.5\text{ mol dm}^{-3}$ stock solution.

(i) Calculate the standard deviation for the $s30\text{ s}$ result at $dm−32.5\text{ mol dm}^{-3}$ HCl. Use the formula:

\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}

Give your answer to 1 decimal place.

(ii) Calculate the initial rate of reaction over the first $s15\text{ s}$ for the result at $dm−30.5\text{ mol dm}^{-3}$ HCl. Include the appropriate unit.