yr1 calculations Flashcards
DEFINITION: The mole
The mole is the amount of substance in grams that has the same number of particles as there are atoms in 12 grams of carbon-12.
DEFINITION: Relative atomic mass
Relative atomic mass is the average mass of one atom compared to one-twelfth of the mass of one atom of carbon-12
DEFINITION: Relative molecular mass
Relative molecular mass is the average mass of a molecule compared to one-twelfth of the mass of one atom of carbon-12
3 equations to calculate moles:
Avogadro’s Constant (L)
There are 6.022 x 1023 atoms in 12 grams of carbon-12. Therefore explained in simpler terms ‘One mole of any specified entity contains 6.022 x 1023 of that entity’:
The equation for Avogadro’s constant
No of particles = moles of substance (in mol) X Avogadro’s constant
Example 3 : How many atoms of Tin are there in a 6.00 g sample of Tin metal?
moles = mass/Ar
= 6.00/ 118.7 = 0.05055 mol
Number atoms = moles x 6.022 x 1023
= 0.05055 x 6.022 x 1023 = 3.04 x1022
density
mass over volume
Empirical formulae
An empirical formula is the simplest ratio of atoms of each element in the compound
Example 7 :
Calculate the empirical formula for a compound that contains 1.82g of K, 5.93g of I and 2.24g of O
Molecular formula from empirical formula
: A molecular formula is the actual number of atoms of each element in the compound
Example 8 : work out the molecular formula for the compound with an empirical formula of C3H6O and a Mr of 116
C3H6O has a mass of 58
The empirical formula fits twice into Mr of 116
So molecular formula is C6H12O2
Hydrated salt
A Hydrated salt contains water of crystallisation
Example 9 Na2SO4 . xH2O has a molar mass of 322.1, Calculate the value of x
x=10
Molar mass xH2O = 322.1 – (23x2 + 32.1 + 16x4) = 180
X = 180/18 =10
Method of heating the crucible
6 steps
- Weigh an empty clean dry crucible and lid.
- Add 2g of hydrated calcium sulfate to the crucible and weigh again
- Heat strongly with a Bunsen for a couple of minutes
- Allow to cool
- Weigh the crucible and contents again
- Heat crucible again and reweigh until you reach a constant mass ( do this to ensure the reaction is complete).
How lid improves accuracy while heating the crucible?
The lid improves the accuracy of the experiment as it prevents loss of solid from the crucible but should be loose fitting to allow gas to escape
Example 10. 3.51 g of hydrated zinc sulfate were heated and 1.97 g of anhydrous zinc sulfate were obtained. Calculate the value of the integer x in ZnSO4 .xH2O
Example 11
Calculate the concentration of solution made by dissolving 5.00 g of Na2CO3 in 250 cm3 water
Example 12
Calculate the concentration of solution made by dissolving 10 kg of Na2CO3 in 0.50 m3 water
Making a solution
11
- Weigh the sample bottle containing the required mass of solid on a 2 dp balance
- Transfer to the beaker and reweigh sample bottle
- Record the difference in mass
- Add 100cm3 of distilled water to the beaker.
Use a glass rod to stir to help dissolve the solid.
- Sometimes the substance may not dissolve well in cold water so the beaker and its contents could be heated gently until all the solid had dissolved.
- Pour the solution into a 250cm3 graduated flask via a funnel.
- Rinse beaker and funnel and add washings from the beaker and glass rod to the volumetric flask.
- make up to the mark with distilled water using a dropping pipette for the last few drops.
- Invert flask several times to ensure a uniform solution.
Remember to fill so the bottom of the meniscus sits on the line on the neck of the flask. With dark liquids like potassium manganate, it can be difficult to see the meniscus
Diluting a solution
- Pipette 25cm3 of original solution into a 250cm3 volumetric flask
- make up to the mark with distilled water using a dropping pipette for the last few drops.
- Invert flask several times to ensure a uniform solution.
Using a volumetric pipette is more accurate than a measuring cylinder because it has a smaller uncertainty
Use a teat pipette to make up to the mark in a volumetric flask to ensure the volume of solution accurately measured and one doesn’t go over the line.
Calculate newly diluted concentration
new diluted concentration = original concentration x original volume over new diluted volume
Example 15
50 cm3 of water are added to 150 cm3 of a 0.20 mol dm-3 NaOH solution. Calculate the concentration of the diluted solution
Example 16
Calculate the volume of water in cm3 that must be added to dilute 5.00 cm3 of 1.00 mol dm−3 hydrochloric acid so that it has a concentration of 0.050 mol dm−3
Example 17:
Calculate the mass of Cl2 gas that has a pressure of 100 kPa, temperature 20 oC , volume 500 cm3 . (R = 8.31)
Example 18:
0.150g of a volatile liquid was injected into a sealed gas syringe. The gas syringe was placed in an oven at 70oC at a pressure of 100kPa and a volume of 80.0cm3 was measured. Calculate the Mr of the volatile liquid (R =8.31)
Using a gas syringe
Example 19
40 cm3 of oxygen and 60 cm3 of carbon dioxide, each at 298 K and 100 kPa, were placed into an evacuated flask of volume 0.50 dm3.
Calculate the pressure of the gas mixture in the flask at 298 K.
Example 20
500 cm3 of methane is combusted at 1atm and 300K. Calculate the volume of oxygen needed to react and calculate the volume of CO2 given off under the same conditions.
Example 21
An important reaction which occurs in the catalytic converter of a car is:
2CO(g) + 2NO(g)—–2CO2 (g) + N2 (g)
In this reaction, when 500 cm3 of CO reacts with 500 cm3 of NO at 650 °C and at 1 atm. Calculate the total volume of gases produced at the same temperature and pressure
Example 22:
Calculate the mass of carbon dioxide produced from heating 5.50 g of sodium hydrogen carbonate. 2NaHCO3—–Na2CO3 + CO2 + H2O
Example 23:
23.6cm3 of H2SO4 neutralised 25.0cm3 of 0.150M NaOH. Calculate the concentration of the
H2SO4 H2SO4 + 2NaOH—–Na2SO4 +2H2O
Example 24:
What is the total volume of gas produced in dm3 at 333K and 100kPa when 0.651 g of magnesium nitrate decomposes when heated? 2Mg (NO3 )2 (s) —-2 MgO(s) + 4NO2 (g) + O2 (g)
Example 25:
Calculate the mass of copper that reacts completely with 150 cm3 of 1.60 mol dm-3 nitric acid
3Cu + 8HNO3—– 3Cu(NO3 )2 + 2NO + 4H2O
Example 26
Calculate the maximum mass of titanium that could be produced from reacting 100 g of TiCl4 with 80.0 g of sodium.
TiCl4 + 4 Na —–4 NaCl + Ti
Calculate percentage yield
Percentage atom economy equation
Example 27:
Calculate the % atom economy for the following reaction where Fe is the desired product assuming the reaction goes to completion.
Example 28:
25.0g of Fe2O3 was reacted and it produced 10.0g of Fe. Calculate the percentage yield.
Fe2O3 + 3CO ——2Fe + 3 CO2
The method for carrying out the titration
- rinse equipment (burette with acid, pipette with alkali, conical flask with distilled water)
- pipette 25 cm3 of alkali into the conical flask
- touch surface of alkali with a pipette ( to ensure the correct amount is added)
- adds acid solution from the burette
- make sure the jet space in the burette is filled with acid
- add a few drops of indicator and refer to a colour change at endpoint
- phenolphthalein [pink (alkali) to colorless (acid): endpoint pink color just disappears] [use if NaOH is used]
- methyl orange [yellow (alkali) to red (acid): endpoint orange] [use if HCl is used]
- use a white tile underneath the flask to help observe the color change
- add acid to alkali whilst swirling the mixture and add acid dropwise at an endpoint
- note burette reading before and after addition of acid
- repeats titration until at least 2 concordant results are obtained- two readings within 0.1 of each other
Recording results
•Results should be clearly recorded in a table
The result should be recorded in full (i.e. both initial and final readings)
•Record titre volumes to 2dp (0.05 cm3 )
Safely dealing with excess acid
Sodium hydrogen carbonate (NaHCO3 ) and calcium carbonate (CaCO3 ) are good for neutralising excess acid in the stomach or acid spills because they are not corrosive and will not cause a hazard if used in excess. They also have no toxicity if used for indigestion remedies but the CO2 produced can cause wind. Magnesium hydroxide is also suitable for dealing with excess stomach acid as it has low solubility in water and is only weakly alkaline so not corrosive or dangerous to drink (unlike the strong alkali sodium hydroxide). It will also not produce any carbon dioxide gas
Common Titration Equations
CH3CO2H + NaOH ——H3CO2 -Na+ + H2O
H2SO4 + 2NaOH——-Na2SO4 +2H2O
HCl + NaOH——-NaCl +H2O
NaHCO3 + HCl ——– NaCl + CO2 + H2O
Na2CO3 + 2HCl ———-2NaCl + CO2 + H2O
Example 29:
A 25.0 cm3 sample of vinegar was diluted in a 250 cm3 volumetric flask
This was then put in a burette and 23.10 cm3 of the diluted vinegar neutralized 25.0 cm3 of 0.100 mol dm-3 NaOH.
Calculate the concentration of the vinegar in g dm-3
Example 30.
An unknown metal carbonate reacts with hydrochloric acid according to the following equation
M2CO3(aq) + 2HCl(aq) ——-2MCl(aq) + CO2(g) + H2O(l)
A 3.96 g sample of M2CO3 was dissolved in distilled water to make 250 cm3 of solution. A 25.0 cm3 portion of this solution required 32.8 cm3 of 0.175 mol dm–3 hydrochloric acid for complete reaction. Calculate the Mr of M2CO3 and identify the metal M
950 mg of impure calcium carbonate tablet was crushed. 50.0 cm3 of 1.00 mol dm–3 hydrochloric acid, an excess, was then added. After the tablet had reacted, the mixture was transferred to a volumetric flask. The volume was made up to exactly 100 cm3 with distilled water. 10.0 cm3 of this solution was titrated with 11.1 cm3 of 0.300 mol dm–3 sodium hydroxide solution. Calculate the percentage of CaCO3 by mass in the tablet
Calculating Apparatus Uncertainties
Reducing uncertainties in a titration
Replacing measuring cylinders with pipettes or burettes which have lower apparatus uncertainty will lower the % uncertainty.
To reduce the % uncertainty in a burette reading it is necessary to make the titre a larger volume.
This could be done by increasing the volume and concentration of the substance in the conical flask or by decreasing the concentration of the substance in the burette.
Reducing uncertainties in measuring mass
Using a balance that measures to more decimal places or using a larger mass will reduce the % uncertainty in weighing a solid. Weighing sample before and after addition and then calculating difference will ensure a more accurate measurement of the mass added.
Calculating the percentage difference between the actual value and the calculated value If we calculated an Mr of 203 and the real value is 214, then the calculation is as follows:
the calculation is as follows:
Calculate difference 214-203 = 11
% = 11/214 x100 =5.41%
