how do you calculate the mole fraction of HCl in an acqueous solution that contains 33.6% HCl by mass?
Ah, calculating mole fraction, a topic that makes everyone go "Avogadro! Avogadro!" Okay, let's put our clown noses on and calculate it.
To find the mole fraction of HCl in the solution, we need to know the mass of HCl and the mass of water in the solution.
We know that the solution is 33.6% HCl by mass, so let's say we have 100g of the solution. That means we have 33.6g of HCl and 66.4g of water.
Now, let's find the moles of HCl:
First, we need to calculate the molar mass of HCl. Hydrogen weighs about 1 gram/mol, and Chlorine weighs about 35.5 grams/mol. So, the molar mass of HCl is 36.5 grams/mol.
To find the moles of HCl, we divide the mass of HCl by its molar mass:
33.6g / 36.5g/mol = 0.92 mol HCl
Next, let's find the moles of water:
The molar mass of water (H2O) is 18 grams/mol.
To find the moles of water, we divide the mass of water by its molar mass:
66.4g / 18g/mol = 3.69 mol water
Finally, let's calculate the mole fraction of HCl:
Mole fraction of HCl = moles of HCl / (moles of HCl + moles of water)
Mole fraction of HCl = 0.92 mol / (0.92 mol + 3.69 mol)
Mole fraction of HCl = 0.20
So, the mole fraction of HCl in the solution is approximately 0.20.
To calculate the mole fraction of HCl in an aqueous solution, you need to follow these steps:
Step 1: Convert the percentage by mass to grams.
Given that the solution contains 33.6% HCl by mass, this means that 33.6 grams of HCl are present in every 100 grams of the solution.
Step 2: Calculate the moles of HCl.
To determine the moles of HCl, you need to divide the mass of HCl by its molar mass. The molar mass of HCl is approximately 36.46 g/mol (1.01 g/mol for hydrogen + 35.45 g/mol for chlorine).
Moles of HCl = mass of HCl / molar mass of HCl
Moles of HCl = 33.6 g / 36.46 g/mol ≈ 0.921 mol
Step 3: Calculate the moles of water.
Since it is an aqueous solution, it implies that water is the solvent. To calculate the moles of water, you can use the formula:
Moles of water = mass of water / molar mass of water
Step 4: Determine the total number of moles in the solution.
To find the total number of moles in the solution, you need to sum the mole amounts of HCl and water calculated in steps 2 and 3.
Total moles in the solution = Moles of HCl + Moles of water
Step 5: Calculate the mole fraction of HCl.
The mole fraction of HCl can now be determined by dividing the moles of HCl by the total moles in the solution.
Mole fraction of HCl = Moles of HCl / Total moles in the solution
Now you have the step-by-step process to calculate the mole fraction of HCl in an aqueous solution that contains 33.6% HCl by mass.
To calculate the mole fraction of a compound in a solution, you need to know the moles of the compound and the total moles of all components in the solution. Here's how you can calculate the mole fraction of HCl in the given aqueous solution:
1. Determine the moles of HCl:
Since we are given the mass percentage of HCl in the solution, you can assume you have 100 grams of the solution. Therefore, the mass of HCl in the solution is 33.6 grams (33.6% of 100g).
To convert the mass of HCl to moles, you need to know the molar mass of HCl, which consists of hydrogen (H) and chlorine (Cl). The molar mass of hydrogen is approximately 1.007 g/mol, and the molar mass of chlorine is approximately 35.453 g/mol.
The molar mass of HCl is the sum of the molar masses of hydrogen and chlorine: 1.007 g/mol + 35.453 g/mol ≈ 36.460 g/mol.
To calculate the moles of HCl, divide the mass of HCl by its molar mass:
moles of HCl = mass of HCl / molar mass of HCl = 33.6 g / 36.460 g/mol ≈ 0.921 mol.
2. Determine the total moles of all components in the solution:
Assuming the solution is dilute and water is the solvent, we can approximate the solution's total volume as equal to its total weight in grams (since the density of water is approximately 1 g/mL).
Therefore, the total weight of the solution is 100 grams (given in the question). Assuming the solution is primarily water, the remaining mass not attributed to HCl is the mass of water in the solution, which is 100 g - 33.6 g = 66.4 g.
Convert the mass of water to moles by dividing by the molar mass of water, which is approximately 18.015 g/mol:
moles of water = mass of water / molar mass of water = 66.4 g / 18.015 g/mol ≈ 3.68 mol.
3. Calculate the mole fraction of HCl:
The mole fraction (X) is given by:
X(HCl) = moles of HCl / total moles of all components in the solution.
Plugging in the values calculated above:
X(HCl) = 0.921 mol / (0.921 mol + 3.68 mol) ≈ 0.200.
Therefore, the mole fraction of HCl in the given aqueous solution that contains 33.6% HCl by mass is approximately 0.200.
33.6% w/w HCl means 33.6 g HCl/100 g solution which means 33.6 g HCl/(33.6g HCl + 66.4 g H2O).
moles HCl = 33.6/molar mass HCl.
moles H2O = 66.4/molar mass H2O.
XHCl = moles HCl/total moles.
XH2O = moles H2O/total moles.