Given the following equation: Na2O + H2O ---> 2 NaOH.
How many grams of NaOH is produced from 1.20 x 10^2 grams of Na2O? How many grams of NaO2 are required to produce 1.60 x 10^2 grams of NaOH?
1.20 x 10^2 grams of Na2O will produce 2.40 x 10^2 grams of NaOH.
1.60 x 10^2 grams of NaOH will require 0.80 x 10^2 grams of Na2O.
To find the number of grams of NaOH produced from a given amount of Na2O, we need to use stoichiometry.
1) How many grams of NaOH is produced from 1.20 x 10^2 grams of Na2O?
1 mole of Na2O reacts with 2 moles of NaOH according to the balanced equation. To determine the molar mass of Na2O and NaOH, we need to know the atomic masses of their constituents: Na (sodium) and O (oxygen).
Na: atomic mass = 22.99 g/mol
O: atomic mass = 16.00 g/mol
The molar mass of Na2O is calculated as:
Na (22.99 g/mol) x 2 + O (16.00 g/mol) = 61.98 g/mol
To convert grams of Na2O to moles, use the formula:
moles of Na2O = grams of Na2O / molar mass of Na2O
moles of Na2O = (1.20 x 10^2 g) / (61.98 g/mol) = 1.94 moles of Na2O
Since the molar ratio between Na2O and NaOH is 1:2, we can determine the moles of NaOH produced with the same formula:
moles of NaOH = moles of Na2O x (2 moles of NaOH / 1 mole of Na2O)
moles of NaOH = 1.94 moles of Na2O x (2 moles of NaOH / 1 mole of Na2O) = 3.88 moles of NaOH
Finally, to convert moles of NaOH to grams, we use the formula:
grams of NaOH = moles of NaOH x molar mass of NaOH
grams of NaOH = 3.88 moles of NaOH x (22.99 g/mol + 16.00 g/mol) = 139.52 g of NaOH
Therefore, 1.20 x 10^2 grams of Na2O will produce 139.52 grams of NaOH.
2) How many grams of NaO2 are required to produce 1.60 x 10^2 grams of NaOH?
In this case, we need to work backward using the stoichiometry of the balanced equation. The molar ratio between NaOH and Na2O is 2:1, which means that for every 2 moles of NaOH, we have 1 mole of Na2O.
To find the moles of NaOH from grams, divide the given mass of NaOH by its molar mass:
moles of NaOH = grams of NaOH / molar mass of NaOH
moles of NaOH = (1.60 x 10^2 g) / (22.99 g/mol + 16.00 g/mol) = 3.52 moles of NaOH
Since the molar ratio between Na2O and NaOH is 1:2, the moles of Na2O needed can be calculated as follows:
moles of Na2O = moles of NaOH x (1 mole of Na2O / 2 moles of NaOH)
moles of Na2O = 3.52 moles of NaOH x (1 mole of Na2O / 2 moles of NaOH) = 1.76 moles of Na2O
Finally, to convert moles of Na2O to grams, we use the formula:
grams of Na2O = moles of Na2O x molar mass of Na2O
grams of Na2O = 1.76 moles of Na2O x 61.98 g/mol = 109.08 g of Na2O
Therefore, 1.60 x 10^2 grams of NaOH requires 109.08 grams of Na2O.
To solve these problems, we will use the concept of stoichiometry, which allows us to calculate the amount of reactants and products in a chemical reaction.
1. Grams of NaOH produced from 1.20 x 10^2 grams of Na2O:
According to the balanced equation, the stoichiometric ratio of NaOH to Na2O is 2:1. This means that for every 2 moles of NaOH, we need 1 mole of Na2O. The molar mass of NaOH is 39.997 grams/mol, and the molar mass of Na2O is 61.9789 grams/mol.
Step 1: Calculate the number of moles of Na2O:
moles of Na2O = mass of Na2O / molar mass of Na2O
moles of Na2O = (1.20 x 10^2 grams) / (61.9789 grams/mol)
moles of Na2O ≈ 1.935 moles
Step 2: Use the stoichiometric ratio to calculate the moles of NaOH produced:
moles of NaOH = moles of Na2O / 1
moles of NaOH ≈ 1.935 moles
Step 3: Calculate the grams of NaOH produced:
grams of NaOH = moles of NaOH × molar mass of NaOH
grams of NaOH ≈ (1.935 moles) × (39.997 grams/mol)
grams of NaOH ≈ 77.4 grams
Therefore, approximately 77.4 grams of NaOH are produced from 1.20 x 10^2 grams of Na2O.
2. Grams of NaO2 required to produce 1.60 x 10^2 grams of NaOH:
To solve this problem, we need to use the balanced equation and the stoichiometry of the reaction:
2 NaO2 + 2 H2O → 4 NaOH + O2
From the equation, we can see that the stoichiometric ratio of NaOH to NaO2 is 4:2 or 2:1. This means that for every 2 moles of NaOH, we need 1 mole of NaO2.
Step 1: Calculate the number of moles of NaOH:
moles of NaOH = mass of NaOH / molar mass of NaOH
moles of NaOH = (1.60 x 10^2 grams) / (39.997 grams/mol)
moles of NaOH ≈ 4.000 moles
Step 2: Use the stoichiometric ratio to calculate the moles of NaO2 required:
moles of NaO2 = moles of NaOH / 2
moles of NaO2 ≈ 2.000 moles
Step 3: Calculate the grams of NaO2 required:
grams of NaO2 = moles of NaO2 × molar mass of NaO2
grams of NaO2 ≈ (2.000 moles) × (61.979 grams/mol)
grams of NaO2 ≈ 124.0 grams
Therefore, approximately 124.0 grams of NaO2 are required to produce 1.60 x 10^2 grams of NaOH.