Given the unbalanced equation:
(NH4)2 CO3-> NH3 + CO2 + H2O
Calculate the mass of ammonia gas that is produced if 1.25g of ammonium carbonate decomposes completely.
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To calculate the mass of ammonia gas produced, we need to determine the molar masses of the substances involved and then use stoichiometry to convert from the given mass of ammonium carbonate to the mass of ammonia gas.
Let's start by finding the molar masses of the compounds involved:
(NH4)2CO3:
- Nitrogen (N) has a molar mass of 14.01 g/mol.
- Hydrogen (H) has a molar mass of 1.01 g/mol.
- Carbon (C) has a molar mass of 12.01 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
Using these values, we can calculate the molar mass of ammonium carbonate:
(2 x 14.01 g/mol) + (8 x 1.01 g/mol) + 12.01 g/mol + (3 x 16.00 g/mol) = 96.09 g/mol
Next, we need to determine the mole ratio between ammonium carbonate and ammonia.
From the balanced equation, we can see that 1 mole of ammonium carbonate produces 2 moles of ammonia. Therefore, the mole ratio is 1:2.
Now, we can calculate the number of moles of ammonium carbonate:
1.25 g * (1 mol/96.09 g) = 0.01299 mol
Since the mole ratio is 1:2, the number of moles of ammonia produced will be twice the number of moles of ammonium carbonate decomposed:
0.01299 mol * 2 = 0.02598 mol
Finally, we can calculate the mass of ammonia gas produced by multiplying the number of moles by the molar mass of ammonia:
0.02598 mol * 17.03 g/mol (molar mass of NH3) = 0.442 g
Therefore, the mass of ammonia gas produced when 1.25 g of ammonium carbonate decomposes completely is 0.442 g.
To calculate the mass of ammonia gas produced, you need to use stoichiometry, which involves calculating the mole ratios between the given substances in the balanced equation.
In this case, the balanced equation is:
(NH4)2CO3 -> 2NH3 + CO2 + H2O
From the equation, you can see that 1 mole of (NH4)2CO3 produces 2 moles of NH3.
Now, let's calculate the moles of (NH4)2CO3 using the given mass of 1.25g. To do this, divide the given mass by the molar mass of (NH4)2CO3.
The molar mass of (NH4)2CO3 is:
(2 x molar mass of NH4) + molar mass of CO3
= (2 x (1 x molar mass of H + 4 x molar mass of N)) + (1 x molar mass of C + 3 x molar mass of O)
Using the periodic table, we find:
Molar mass of H = 1.008 g/mol
Molar mass of N = 14.007 g/mol
Molar mass of C = 12.011 g/mol
Molar mass of O = 15.999 g/mol
Plugging in these values, we get:
Molar mass of (NH4)2CO3 = (2 x (1.008 g/mol) + 4 x (14.007 g/mol)) + (12.011 g/mol + 3 x 15.999 g/mol)
= (2.016 g/mol + 56.028 g/mol) + (12.011 g/mol + 47.997 g/mol)
= 58.044 g/mol + 60.008 g/mol
= 118.052 g/mol
Now, calculate the moles of (NH4)2CO3:
moles = mass / molar mass
= 1.25 g / 118.052 g/mol
≈ 0.0106 mol
Since the mole ratio of (NH4)2CO3 to NH3 is 1:2, this means that:
0.0106 mol (NH4)2CO3 x (2 mol NH3 / 1 mol (NH4)2CO3) = 0.0212 mol NH3
Finally, to find the mass of ammonia gas produced, multiply the number of moles of NH3 by its molar mass, which is approximately 17.031 g/mol:
mass = moles x molar mass
= 0.0212 mol NH3 x 17.031 g/mol
≈ 0.361 g
Therefore, approximately 0.361 grams of ammonia gas will be produced if 1.25 grams of ammonium carbonate decomposes completely.