Calculate the mass of marble chips that produce 20 grams of carbon (iv) oxide .when reacted with dilute hydrochloric acid (c=12,O=16,Ca=40)
To calculate the mass of marble chips needed to produce 20 grams of carbon dioxide (CO2) when reacted with hydrochloric acid, you'll need to use the balanced chemical equation for the reaction and the molar masses of the relevant substances.
The reaction between marble chips (calcium carbonate, CaCO3) and hydrochloric acid (HCl) produces carbon dioxide gas (CO2), water (H2O), and calcium chloride (CaCl2). The balanced chemical equation is:
CaCO3 + 2HCl → CO2 + H2O + CaCl2
Firstly, we need to determine the molar mass of carbon dioxide (CO2). Carbon has a molar mass of 12.01 g/mol, and oxygen has a molar mass of 16.00 g/mol. Since there are two oxygen atoms in carbon dioxide, we calculate the molar mass as follows:
Molar mass of CO2 = (2 × molar mass of O) + molar mass of C
Molar mass of CO2 = (2 × 16.00 g/mol) + 12.01 g/mol
Molar mass of CO2 = 32.00 g/mol + 12.01 g/mol
Molar mass of CO2 = 44.01 g/mol
Now we can set up a ratio between the moles of CO2 and the moles of calcium carbonate using the balanced equation. According to the equation, one mole of CaCO3 produces one mole of CO2:
1 mole CaCO3 : 1 mole CO2
To find the moles of CO2 produced, we divide the mass of CO2 (20 grams) by its molar mass:
Moles of CO2 = Mass of CO2 / Molar mass of CO2
Moles of CO2 = 20 g / 44.01 g/mol
Moles of CO2 ≈ 0.454 moles
Since one mole of calcium carbonate produces one mole of CO2, the moles of CaCO3 consumed will also be 0.454 moles.
Now we can calculate the mass of calcium carbonate needed using its molar mass (40.08 g/mol):
Mass of CaCO3 = Moles of CaCO3 × Molar mass of CaCO3
Mass of CaCO3 = 0.454 moles × 40.08 g/mol
Mass of CaCO3 ≈ 18.16 grams
Therefore, approximately 18.16 grams of marble chips (calcium carbonate) will produce 20 grams of carbon dioxide when reacted with hydrochloric acid.