Gas volume answer 4c

Analysis and evaluation exercise

0.315 g of the solid carbonate was used. 10 cm³ of 1.0 M hydrochloric acid was injected through the septum. An initial gas volume of 56 cm³ was measured. On shaking the solution further gas was released, giving a final figure of 62 cm³.

Use the results to determine the most likely formula for the unknown carbonate. Carry out an error analysis on the experiment and suggest possible improvements.

Analysis

Allowing for the addition of 10 cm³ of acid:

Volume of CO₂ = 62 - 10 = 52 cm³

Number of moles of CO₂ = 52/24000 = 0.00217 mol

CO₃^2- º CO₂

\ number of moles of CO₃^2- = 0.00217 mol

\ molar mass of carbonate = 0.315/0.00217 = 145.4

Comparing to known carbonates:

Na₂CO₃ = 106, K₂CO₃ = 138, Rb₂CO₃ = 231, MgCO₃ = 84, CaCO₃ = 100

This suggests that K₂CO₃ is the formula of the unknown carbonate

This shows the importance of proper error analysis. If I had included SrCO₃ = 148 in the list we would probably have chosen it as the correct answer (it's the closest to our answer of 148). The following error analysis will show how we might have come to the correct answer.

Error analysis

The error in the balance is ± 0.002 g as we weighed by difference involving two weighings. This gives a percentage error of 0.002/0.315 × 100 = ± 0.63%.

The gas syringe markings are quite accurate, but most syringes have a degree of stickiness. This allows the plunger to be moved in and out by 2 or 3 cm³, with the correct reading probably being somewhere near the middle of this movement. Given this, it is unlikely that the syringe is accurate to more than ± 1 cm³. This gives a percentage error of 1/62 = ± 1.6%.

The markings on the syringe used to inject the hydrochloric acid are not particularly accurate. An error of ± 0.5 cm³ is likely. This gives an error of 0.5/10 × 100 = ± 5%. However, this is where we need to be careful. Whilst this is the error of that measurement, it does not give a 5% error in the final result. It only introduces a further ± 0.5 cm³ uncertainty in the gas syringe reading. This means the gas syringe error is actually ± 1.5 cm³ , giving a percentage error of 1.5/62 = ± 2.4%.

This gives a total measurable error of ± 3.0%. This means that our answer of 145.4 could actually lie between 141.0 and 149.8. This does not include the accepted answer of 138. As mentioned above, had we included SrCO₃, it would have probably led us to conclude incorrectly that this was the right answer. This is why it is important to consider other non-measurement errors and the effect that they would have on the final answer.

We have assumed that the apparatus is at room temperature and pressure (we could, of course, always have measured the temperature and pressure!). However, it is unlikely that either is far out, so this should only introduce a very small error. Without measurement, we cannot say whether this would increase or decrease the final answer. For example, if the pressure were lower than normal we would have measured a larger volume. This would have suggested more moles and, hence, a smaller molar mass.

Impurity of the sample is likely to mean there is less carbonate present (unless the impurity is a lighter carbonate!). This would gives a smaller gas volume and, therefore, a greater molar mass.

Any gas loss through leakage of the apparatus would give a smaller gas volume leading to a greater molar mass calculation.

We saw that a significant quantity of CO₂ was released on shaking. However, some carbon dioxide will still be dissolved in the acid. This gives a smaller volume of collected gas and, hence, a greater molar mass.

We can see that all the non-measurement errors lead to us over-estimating the molar mass of the carbonate. It is therefore highly likely that the correct molar mass is less than that calculated. This would lead us too believe that the lower figure of 138 for the K₂CO₃ is the most likely answer.

Improvements

Greater accuracy of equipment would reduce the measurement errors. For example, using a balance which measures to the nearest 0.0001 gram would reduce the error from 0.63% to 0.063%.

We could measure the solubility of carbon dioxide gas in the final solution so that an allowance could be made for it.