When heated at high temperature, sodium carbonate, Na2CO3decomposes to sodium oxide and carbon dioxide gas. A sample of 587.3 mL gas was collected using water displacement method at 27 °C at a total pressure of 760 mm Hg and vapour pressure of water is 28 mm Hg.
a) calculate the mass of carbon oxide collected
b) calculate the mass of sodium carbonate decomposed
Na2CO3 ==> Na2O + CO2
PV = nRT for the CO2 gas
Ptotal = PCO2 + PH2O You know Ptotal and you are given PH2O. Make sure you watch the units and solve for PCO2, preferable in mm Hg, then convert to atmospheres by atm = pressure in mm/760. Use that for P in the formula. Solve for n = number of moles.
Then mols = grams/molar mass. You know mols and molar mass, solve for grams which is the answer to a.
b. Using the coefficients in the balanced equation, convert mols CO2 to mols Na2CO3. Note that 1 mol CO2 comes from 1 mol Na2CO3.
Then mols Na2CO3 x molar mass Na2CO3 = grams Na2CO3.
Post your work if you get stuck.
To calculate the mass of carbon dioxide collected, we need to use the ideal gas law equation: PV = nRT, where P is the total pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures to Kelvin: 27 °C + 273.15 = 300.15 K.
We have the following information:
- Total pressure, P = 760 mm Hg
- Vapour pressure of water, P(water) = 28 mm Hg (this needs to be subtracted from the total pressure)
- Volume, V = 587.3 mL (this needs to be converted to liters)
- T = 300.15 K
a) To calculate the mass of carbon dioxide collected, we need to determine the number of moles using the ideal gas law equation:
PV = nRT.
- P = (760 mm Hg - 28 mm Hg) = 732 mm Hg (since we subtract the vapour pressure of water)
- V = 587.3 mL = 0.5873 L
- R = 0.0821 L·atm/(mol·K) (this is the ideal gas constant)
- T = 300.15 K
Now we can rearrange the equation to solve for n (number of moles): n = PV / RT.
n = (732 mm Hg * 0.5873 L) / (0.0821 L·atm/(mol·K) * 300.15 K)
n = 15.42 mol
The balanced equation tells us that 1 mole of sodium carbonate produces 1 mole of carbon dioxide. Therefore, the mass of carbon dioxide collected is the same as the molar mass of carbon dioxide (44.01 g/mol) multiplied by the number of moles:
Mass of carbon dioxide collected = 15.42 mol * 44.01 g/mol
b) To calculate the mass of sodium carbonate decomposed, we need to use the molar mass of sodium carbonate (Na2CO3). It is:
(2 * atomic mass of Na) + atomic mass of C + (3 * atomic mass of O)
= (2 * 22.99 g/mol) + 12.01 g/mol + (3 * 16.00 g/mol)
= 105.99 g/mol
The mass of sodium carbonate decomposed is then:
Mass of sodium carbonate decomposed = 15.42 mol * 105.99 g/mol
Please perform the calculations to find the final answers for both parts (a) and (b).
To calculate the mass of carbon dioxide gas (CO2) collected, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin: 27 °C + 273.15 = 300.15 K
Now we can calculate the number of moles of CO2 using the ideal gas law equation:
n = (PV) / (RT)
n = ((760 mm Hg - 28 mm Hg) * 587.3 mL) / (0.0821 L*atm/mol*K * 300.15 K)
Note: We convert the pressure from mm Hg to atm and the volume from mL to L to ensure consistent units.
Next, we'll convert the volume from mL to L:
V = 587.3 mL / 1000 mL/L = 0.5873 L
Plugging in the values:
n = ((760 - 28) * 0.5873) / (0.0821 * 300.15)
Calculate n to find the number of moles of CO2 collected.
Once we have the number of moles of CO2, we can calculate its mass using the molar mass of CO2, which is 44.01 g/mol.
Finally, multiply the number of moles of CO2 by its molar mass to determine the mass of carbon dioxide collected.
Part a) Calculate the mass of carbon dioxide collected.
To calculate the mass of sodium carbonate decomposed, we need to use stoichiometry and the balanced chemical equation for its decomposition.
The balanced chemical equation for the decomposition of sodium carbonate (Na2CO3) into sodium oxide (Na2O) and carbon dioxide (CO2) is:
Na2CO3 -> Na2O + CO2
We can see from the balanced equation that the mole ratio between Na2CO3 and CO2 is 1:1.
Therefore, the moles of Na2CO3 decomposed will be equal to the moles of CO2 collected.
Once again, calculate the number of moles of Na2CO3 decomposed using the ideal gas law equation:
n = (PV) / (RT)
Plug in the values of pressure, volume, gas constant, and temperature.
Finally, multiply the number of moles of Na2CO3 decomposed by its molar mass to determine the mass of sodium carbonate decomposed.
Part b) Calculate the mass of sodium carbonate decomposed.
Remember to use units consistently throughout the calculations and convert appropriately.