K2co3.xh2o weighted in 10,5 gramms reacted with chloride acid till there are no more k2co3.xh20 . Co2 was volumed 1.12 litres (0 celsius, 1 atmosphere). Determine how the number of x is!
To determine the value of x in K2CO3.xH2O, we need to use the information given in the question.
1. Calculate the number of moles of CO2 formed:
We know that 1 mole of CO2 occupies 22.4 liters at 0 degrees Celsius and 1 atmosphere of pressure. Since 1.12 liters of CO2 is produced, we can calculate the number of moles:
moles of CO2 = volume of CO2 / molar volume of CO2 at STP
moles of CO2 = 1.12 / 22.4
moles of CO2 = 0.05 moles
2. Determine the number of moles of K2CO3:
The molar mass of K2CO3 is calculated as follows:
Molar mass of K = 39.10 g/mol
Molar mass of C = 12.01 g/mol
Molar mass of O = 16.00 g/mol
Molar mass of K2CO3 = (2 * molar mass of K) + molar mass of C + (3 * molar mass of O)
Molar mass of K2CO3 = (2 * 39.10) + 12.01 + (3 * 16.00)
Molar mass of K2CO3 = 138.21 g/mol
Using the given weight of K2CO3 (10.5 grams), the number of moles of K2CO3 can be calculated:
moles of K2CO3 = weight of K2CO3 / molar mass of K2CO3
moles of K2CO3 = 10.5 / 138.21
moles of K2CO3 = 0.076 moles
3. Determine the number of moles of H2O:
Using the balanced chemical equation for the reaction:
K2CO3 + 2HCl → 2KCl + H2O + CO2
We know that 1 mole of K2CO3 reacts with 1 mole of H2O. Therefore, the number of moles of H2O is the same as the number of moles of K2CO3, which is 0.076 moles.
4. Calculate the mass of H2O in the sample:
The molar mass of H2O is 18.015 g/mol. Using the number of moles of H2O, we can calculate the mass:
mass of H2O = moles of H2O * molar mass of H2O
mass of H2O = 0.076 * 18.015
mass of H2O = 1.369 g
5. Calculate the number of moles of x in K2CO3.xH2O:
Since we know that the total weight of the K2CO3.xH2O sample is 10.5 grams and the mass of H2O is 1.369 grams, we can calculate the mass of K2CO3 (xH2O) as follows:
mass of K2CO3 (xH2O) = total weight - mass of H2O
mass of K2CO3 (xH2O) = 10.5 - 1.369
mass of K2CO3 (xH2O) = 9.131 g
Now we can calculate the number of moles of K2CO3 (xH2O):
moles of K2CO3 (xH2O) = mass of K2CO3 (xH2O) / molar mass of K2CO3 (xH2O)
moles of K2CO3 (xH2O) = 9.131 / 138.21
moles of K2CO3 (xH2O) ≈ 0.066 moles
6. Determine the value of x:
To find the value of x, we need to calculate the molar ratio between K2CO3 and xH2O by comparing the moles of K2CO3 and K2CO3 (xH2O):
moles of K2CO3 / moles of K2CO3 (xH2O) = coefficient of K2CO3 / coefficient of K2CO3 (xH2O)
From the balanced equation, we know that the coefficient of K2CO3 is 1 and the coefficient of K2CO3 (xH2O) is 1 as well. Therefore:
0.076 / 0.066 = 1 / x
Cross-multiplying:
0.076x = 0.066
Solving for x:
x ≈ 0.868
Therefore, the value of x in K2CO3.xH2O is approximately 0.868.
To determine the number of x in the formula K2CO3·xH2O, we need to calculate the moles of CO2 produced during the reaction.
Step 1: Convert the given mass of K2CO3·xH2O to moles.
The molar mass of K2CO3 is calculated as follows:
K: (2 * 39.10 g/mol) = 78.20 g/mol
C: 12.01 g/mol
O: (3 * 16.00 g/mol) = 48.00 g/mol
H: 1.01 g/mol
Therefore, the molar mass of K2CO3 is:
(78.20 g/mol) + (12.01 g/mol) + (48.00 g/mol) = 138.21 g/mol
The molar mass of H2O is calculated as follows:
H: (2 * 1.01 g/mol) = 2.02 g/mol
O: 16.00 g/mol
Therefore, the molar mass of H2O is:
2.02 g/mol + 16.00 g/mol = 18.02 g/mol
Now, we can determine the moles of K2CO3·xH2O by dividing the given mass by its molar mass:
Moles of K2CO3·xH2O = (10.5 g) / (138.21 g/mol) = 0.0758 mol
Step 2: Determine the moles of CO2 produced.
From the balanced equation, we know that 1 mole of K2CO3 produces 1 mole of CO2.
Therefore, the moles of CO2 is also equal to 0.0758 mol.
Step 3: Use the ideal gas law to calculate the volume of CO2.
The ideal gas law is represented as follows:
PV = nRT
Where:
P = Pressure (1 atm)
V = Volume (in liters)
n = moles of gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
Given:
P = 1 atm
V = 1.12 L
n = 0.0758 mol
R = 0.0821 L·atm/mol·K
T = 0 °C = 273.15 K (Convert to Kelvin by adding 273.15)
Substituting the values into the ideal gas law equation:
(1 atm) * (1.12 L) = (0.0758 mol) * (0.0821 L·atm/mol·K) * (273.15 K)
Simplify the equation:
1.12 L = 1.98 L·atm
Now, divide both sides by 1.98 to isolate the volume:
V = 1.12 L / 1.98 L·atm ≈ 0.5666 atm·L/mol
Step 4: Determine the moles of H2O.
From the balanced equation, we know that 1 mole of K2CO3·xH2O produces 1 mole of CO2.
Therefore, the moles of H2O is also equal to 0.0758 mol.
Step 5: Calculate the number of x by comparing the moles of CO2 and H2O.
Since each mole of K2CO3·xH2O produces one mole of CO2 and one mole of H2O, the number of x is equal to the ratio of the moles of H2O to the moles of CO2:
x = moles of H2O / moles of CO2
x = 0.0758 mol / 0.0758 mol
x = 1
Therefore, the number of x in the formula K2CO3·xH2O is 1.