A 495-mL sample of unknown HCl solution reacts completely with Na2CO3 to form 18.1g CO2. What was the concentration of the HCl solution?
Well, that's a lot of numbers! It seems like even HCl and Na2CO3 can't escape the world of mathematics. But fear not, I'm here to clown around and help you out!
First, let's convert the mass of CO2 to moles. The molar mass of CO2 is approximately 44 g/mol, so 18.1 g CO2 would be about 0.412 moles.
Since HCl and Na2CO3 react in a 1:1 ratio, the moles of HCl present in the solution would also be 0.412 moles.
Now, let's calculate the concentration of the HCl solution. Concentration is typically expressed in moles per liter (M). In this case, we have 495 mL of solution, which is equal to 0.495 L.
Dividing the moles of HCl (0.412) by the volume in liters (0.495), we get a concentration of HCl of approximately 0.832 M.
So, the concentration of the HCl solution is 0.832 M. Now, wasn't that a breath of fresh air?
To find the concentration of the HCl solution, we need to determine the number of moles of HCl and then divide it by the volume of the solution.
Let's calculate the number of moles of CO2 produced first.
Step 1: Find the molar mass of CO2
The molar mass of CO2 is calculated by adding the atomic masses of carbon (C) and two oxygen (O) atoms.
Molar mass of CO2 = 12.01 g/mol + 16.00 g/mol + 16.00 g/mol = 44.01 g/mol
Step 2: Calculate the number of moles of CO2
The number of moles of CO2 can be found using the formula:
moles = mass / molar mass
moles of CO2 = 18.1 g / 44.01 g/mol = 0.411 mol
Step 3: Recognize the stoichiometry ratio between HCl and CO2
According to the balanced chemical equation for the reaction between HCl and Na2CO3, we know that 2 moles of HCl react with 1 mole of CO2.
Step 4: Calculate the number of moles of HCl
Using the stoichiometry ratio calculated in step 3, we can determine the number of moles of HCl.
moles of HCl = 2 * moles of CO2 = 2 * 0.411 mol = 0.822 mol
Step 5: Calculate the concentration of HCl
The concentration of HCl is given in moles per liter (M).
Concentration = moles / volume
Given that the volume of the solution is 495 mL, we need to convert it to liters:
Volume = 495 mL * (1 L / 1000 mL) = 0.495 L
Now, we can calculate the concentration:
Concentration = 0.822 mol / 0.495 L = 1.66 M
Therefore, the concentration of the HCl solution is 1.66 M.
To determine the concentration of the HCl solution, we need to first calculate the number of moles of CO2 produced in the reaction.
The balanced equation for the reaction between HCl and Na2CO3 is:
2HCl + Na2CO3 -> 2NaCl + H2O + CO2
From the balanced equation, we can see that 2 moles of HCl react to produce 1 mole of CO2. Therefore, the number of moles of CO2 can be calculated using the given mass of CO2:
Number of moles of CO2 = mass of CO2 / molar mass of CO2
The molar mass of CO2 is approximately 44.01 g/mol.
Number of moles of CO2 = 18.1 g / 44.01 g/mol ≈ 0.411 moles
Since 2 moles of HCl produce 1 mole of CO2, the number of moles of HCl can be calculated as:
Number of moles of HCl = 0.411 moles / 2 ≈ 0.206 moles
Now, we can determine the concentration of the HCl solution (in moles per liter):
Concentration of HCl = Number of moles of HCl / Volume of solution
Volume of solution = 495 mL = 0.495 L
Concentration of HCl = 0.206 moles / 0.495 L ≈ 0.416 M
Therefore, the concentration of the HCl solution is approximately 0.416 M.