Quantitative analysis and uncertainty

Titration and rate data, calculations, and combining measurement uncertainties.

A student investigates the effect of temperature on the rate of reaction between sodium thiosulfate and hydrochloric acid by timing how long it takes for a cross under the flask to disappear. At $25\,^\circ\text{C}$ the time was $64\,\text{s}$ ; at $35\,^\circ\text{C}$ it was $30\,\text{s}$ .

(a) Calculate the relative rate ( $1/t$ ) at each temperature and the factor by which the rate increased.

(b) Suggest one reason why the times may be inaccurate, other than a timing reaction-time error.

(a) $1/t = 0.0156\,\text{s}^{-1}$ at $25\,^\circ\text{C}$ and at (1)

To find the purity of a sample of limestone, $1.25\,\text{g}$ of the powdered rock was added to $50.0\,\text{cm}^3$ of $1.00\,\text{mol dm}^{-3}$ hydrochloric acid (an excess). When the fizzing stopped, the mixture was made up to with distilled water. portions of this solution were titrated with sodium hydroxide; the mean titre was .

$n(\text{NaOH}) = 0.02640 \times 0.100 = 2.64 \times 10^{-3}\,\text{mol}$ , equal to $n(\text{HCl})$ in $25.0\,\text{cm}^3$ (1)
$n(\text{HCl})$ remaining in $250.0\,\text{cm}^3 = 0.0264\,\text{mol}$ (1)
$n(\text{HCl})$ added at the start $= 0.0500 \times 1.00 = 0.0500\,\text{mol}$ (1)
$n(\text{HCl})$ reacted $= 0.0236\,\text{mol}$ , so $n(\text{CaCO}_3) = 0.0118\,\text{mol}$ (1)
Mass of $\text{CaCO}_3 = 0.0118 \times 100.1 = 1.18\,\text{g}$ (1)
Percentage $= 1.18 \div 1.25 \times 100 = 94.5\%$ (1)

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