Anonymous
Anonymous asked in Science & MathematicsChemistry · 9 years ago

# A 1.056 sample of limestone produces 284 mL of CO2 @STP. what is the mass % of CaCO3 is in the original sample?

a sample of limestone and other solid materials is heated and the limestone decomposes to give calcium oxide and carbon dioxide:

CaCO3 ----> CaO + CO2

a 1.506 g sample of limestone containing material produces 284 mL of CO2 at STP. what is the mass percent of CaCO3 is in the original sample?

Please show work, I have been having a really hard time with this. Thanks

Relevance

So far , quite a number of different answers - can it be that difficult?

Balanced equation:

CaCO3 → CaO + CO2

1mol CaCO3 produces 1 mol CO2

At STP, 1 mol CO2 = 22.4 litres

At STP , 0.284 L CO2 = 0.284/22.4 = 0.01268 mol CO2

This came from decomposition of 0.01268 mol CaCO3

Molar mass CaCO3 = 100g/mol

0.01268 mol = 0.01268*100 = 1.268g CaCO3 in sample

% CaCO3 in original sample = 1.268/1.506 *100 = 84.2% CaCO3 in sample.

Now at least you have 2 correct answers that agree and ( at last count) 3 incorrect answers.

• First of all we need to look at the decomposition equation of limestone. We see that calcium carbonate (calcite) decomposes in a 1:1 ratio to CaO and CO2 - i.e. for every mole of CaCO3 you decompose you will produce 1 mole of CaO and 1 mole of CO2.

Knowing this we can use the number of moles of CO2 produced as evidence for the number of moles CaCO3 in the original sample (because these values will be the same). If we can assume that CO2 is an ideal gas (usually the case), we can say:

PV = nRT (this is the ideal gas equation)

P = pressure, V = volume, n = Number of Moles (what we will solve for), R = ideal gas constant, T = temperature. At STP we know that P = 100,000 Pa and T = 273.15 K, and we are given volume and R is a constant, therefore we can solve for n.

Firstly however, if we are going to use P in pascals, T in k, R in J/mole*k, and n in moles (units), then we need to have the volume in cubic meters. Therefore:

V = 284 mL = 284 cm cubed

284 cm cubed * 10 to the negative 6 meters cubed per cm cubed = 0.000284 meters cubed.

Now we can rearrange the gas law to solve for n,

n = PV / RT = (100,000*0.000284) / (8.314510*273.15) = 0.0125 moles

note: do not worry about where the 8.314510 came from it is just a constant.

Because we know that the reaction produced 0.0125 moles of CO2, we know that there must have been this amount of calcite in the original sample. Therefore if we multiply this number by the molecular weight of calcite we will get the number of grams of calcite in the original sample - i.e.:

0.0125 moles * 100.09 g / mole = 1.25 g

Therefore we had 1.25 g CaCO3 in our original sample. Therefore the mass percentage is given by:

MP% = mass CaCO3 / mass sample * 100%

= 1.25 g / 1.506 g * 100% = 83.11% (by mass)

• 284 mL = 0.284 L CO2. At STP 1 mol occupies 22.4 L. 0.284 / 22.4 = 0.01268 mol CO2.

CO2 / CaCO3 ratio is 1 / 1.

0.01268 mol CaCO3 * mol mass CaCO3 = 0.01268 mol * 100 g/mol = 1.268 g CaCO3.

CaCO3 mass / limestone mass * 100 = 1.268 / 1.506 * 100 = 84.2% CaCO3.

• first you balance the equation:

CaCO3------->CaO + CO2

they all react in a 1 to 1 mole ratio

since 284 mL of teh gas was produced at STP, you determine the number of moles of CO2

1 mole CO2 = 22.4dm3

x moles CO2=0.284dm3

0.284/22.4=0.013 moles

hence 0.013 moles of calcium carbonate was in teh original sample, to find the mass of calcium carbonate

0.013 * 100=.1.3grams

1.3/1.506 * 100= 86.32%

• 79.8% :)

since 22.4 l ( or dm3) of any gas equals to one mole of the gas under STP.. we can calculate the number of moles of CO2 = 0.012 moles..

from the equation we can see the mole ration between CO2 and CaCO3 is 1:1..

hence number of moles of CaCO3 is also 0.012..

from the molecular mass of calcium carbonate.. we can get the mass of caco3

since 1 moles has the mass of 100.1 ( ca + c + 3O)

0.012 has the mass of 1.2012..

1.2012 / 1.506 x 100 = 79.8% :) :) Hope I helped..