If 157 mL of C2H2(g) is collected over water at 22℃ and a barometric pressure of 745 torr, how many grams of CaC2 (s) have been consumed?

Question

Acetylene gas, (C2H2 (g),) can be produced by the reaction of calcium carbide with water:  

CaC2 (s)  + 2H2O (l)  ------------>  Ca(OH)2 (s)  + C2H2(g)

Answer 1

Vapor pressure of H₂O at 22ºC = 19.8 torr

P of C₂H₂ = 745 torr - 19.8 torr = 725.2 torr (note: you must subtract the vapor pressure of water)

Find the moles of C₂H₄ using the ideal gas law:

PV = nRT

n = PV/RT = (725.2 torr)(0.157 L)/(62.36 L-torr/Kmol)(295K)

n = 0.006189 moles C₂H₂

moles CaC₂ = 0.006189 moles since there is a 1:1 ratio between CaC₂ and C₂H₂

mass CaC₂ = 0.006189 moles x 64.1 g/mol = 0.397 g of CaC₂ consumed

Answer 2

Dear Jadyn,

Thank you for your questions!

This is a stoichiometry problem with gas. As such, in order to answer it, you need to find the amount of moles of C₂H₂ gas collected using formula PV=nRT, where n = PV/RT

**EDIT** Because gas was collected over water, the total pressure of 745 torr is a total of two gases: C₂H₂ and vapors of H₂O. In order to know the pressure of C2H2, we need to subtract the vapor pressure of H₂O at 22^oC from total pressure: 745 - 19.8torr = 725.2 torr ** Thank you to J.R.S for pointing it out.

Our data however is not given in proper units. The pressure provided is in torr, so it will need to be converted to atm first. Considering that there is 760 torr in 1 atm, we can conclude that 725.2torr/760 = 0.95atm. Additionally, volume needs to be converted to liters by dividing 157mL/1000 and temperature needs to be converted to Kelvin by adding 273 to 22^oC. The new sets are: P = 0.98atm; V=0.157L and T=295K.

Once plugged in, n = 0.95atm x 0.157L / 0.0821 x 295 = 0.0616 moles of C₂H₂

Once we found moles of product, we can use stoichiometric ratio to find CaC_2. Being that the ratio is 1:1, 0.0635moles of C₂H₂ will result from 0.0616 moles of CaC₂

To convert moles to grams, we need the molar mass of CaC₂. We can find it by adding molar masses of calcium and sulfur: Molar Mass = Ca+2C=40+24=64g/mol

The mass of CaC₂ is moles x Molar Mass = 0.0616mol x 104 g/mol = 0.39 grams

I hope that helped.

Best,

Riana