What is [H3O+] in a solution obtained by dissolving 215 mL HCl(g), measured at 23 degrees C and 757 mmHg, in 4.30 L of aqueous solution?
Use PV = nRT and calculate n = number of moles HCl. Don't forget to change mL to liters and T to Kelvin.
That will give you moles. The molarity = mols/L solution = moles/4.30 = ?? molarity of the final solution.
To determine the concentration of H3O+ in the solution, we need to consider the dissociation of HCl in water. HCl dissociates into H+ and Cl- ions:
HCl (g) + H2O → H+ (aq) + Cl- (aq)
To find the concentration of H3O+, we need to calculate the number of moles of HCl and then use it to determine the concentration in moles per liter.
First, let's calculate the number of moles of HCl:
Using the ideal gas law equation:
PV = nRT
Where:
P = pressure = 757 mmHg = 0.997 atm (converted from mmHg to atm using the conversion factor 1 atm = 760 mmHg)
V = volume = 215 mL = 0.215 L (converted from mL to L)
n = number of moles
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature = 23°C = 23 + 273 = 296 K
0.997 atm × 0.215 L = n × 0.0821 L·atm/(mol·K) × 296 K
n = (0.997 × 0.215) / (0.0821 × 296)
n ≈ 0.00238 moles
We have 0.00238 moles of HCl.
Now, let's calculate the concentration of H3O+ in moles per liter:
The volume of the solution is given as 4.30 L.
Concentration (in moles/L) = moles of solute / volume of solution
Concentration = 0.00238 moles / 4.30 L
Concentration ≈ 0.000551 moles/L.
Therefore, the concentration of [H3O+] in the solution obtained by dissolving 215 mL HCl(g) in 4.30 L of aqueous solution is approximately 0.000551 moles/L.