What volume of HCl gas at 25â—¦ C and 1 atm should be bubbled into 375 mL of a 0.680 M aqueous solution of HClO4 so that the pH of the resulting solution is 0? Assume that all the HCl dissolves and that
the volume of the solution does not change with the addition of HCl.
How many mols do we have in the HClO4. That's M x L = 0.680*.375 = about 0.250 but you need to be more accurate than that.
How much acid do you need to add to make pH = 0. pH = 0 means 1.0M H^+.
mols desired = M x L = 1.0 x 0.375L = 0.375 mols.
Difference is 0.375-0.250 = about 0.125 mols.
Use PV = nRT to solve for volume of HCl gas at the conditions listed.
To determine the volume of HCl gas required, we need to calculate the moles of HClO4 in the solution and then find the moles of HCl needed to achieve a pH of 0.
Step 1: Calculate the moles of HClO4 in the solution.
moles of HClO4 = volume (in liters) x concentration
moles of HClO4 = 375 mL x (1 L / 1000 mL) x 0.680 M
moles of HClO4 = 0.255 mol
Step 2: Calculate the moles of HCl needed to achieve a pH of 0.
Since the pH is given as 0, we can assume that all of the HClO4 has dissociated into H+ and ClO4- ions.
Since HCl is a stronger acid than HClO4, we can assume that all the HClO4 has converted into HCl by the reaction:
HClO4(aq) + H2O(l) -> H3O+(aq) + ClO4-(aq)
Therefore, the moles of HCl needed is equal to the moles of HClO4 in the solution:
moles of HCl = 0.255 mol
Step 3: Calculate the volume of HCl gas at 25°C and 1 atm.
To convert moles of HCl to volume, we can use the ideal gas law:
PV = nRT
R = 0.0821 L x atm / (mol x K) (the ideal gas constant)
T = 25°C + 273.15 = 298.15 K (convert temperature to Kelvin)
P = 1 atm (pressure)
Volume (V) = (n x R x T) / P
Volume (V) = (0.255 mol HCl x 0.0821 L x atm / (mol x K) x 298.15 K) / 1 atm
Volume (V) = 6.28 L
Therefore, to achieve a pH of 0, approximately 6.28 liters of HCl gas should be bubbled into the 375 mL solution of HClO4.
To find the volume of HCl gas needed to achieve a pH of 0 in the resulting solution, we need to use the concept of molarity and the dissociation of HCl in water.
Here's how you can solve this problem step by step:
Step 1: Write the dissociation equation for HCl in water:
HCl(g) + H2O(l) → H3O+(aq) + Cl-(aq)
Step 2: Calculate the moles of H3O+ required to achieve a pH of 0. Since pH is defined as -log[H3O+], a pH of 0 corresponds to a concentration of [H3O+] = 1 M.
Step 3: Since the concentration of H3O+ is the same as the concentration of HCl, we can directly calculate the moles of HCl using the formula:
moles = concentration x volume
moles of HCl = 1 M x (375 mL / 1000 mL/L) = 0.375 mol
Step 4: By stoichiometry, we know that 1 mole of HCl(g) produces 1 mole of H3O+. Therefore, the number of moles of HCl gas needed is 0.375 mol.
Step 5: Use the ideal gas law equation to calculate the volume of HCl gas needed:
PV = nRT
Re-arranging the equation, V = (nRT) / P, where:
V = volume of gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (convert 25°C to Kelvin by adding 273.15)
P = pressure (1 atm)
Temperature in Kelvin = 25°C + 273.15 = 298.15 K
V = (0.375 mol x 0.0821 L·atm/(mol·K) x 298.15 K) / 1 atm
Calculating this equation gives you the volume of HCl gas needed.
Note: Ensure your units are consistent throughout the calculations. In this case, temperature is in Kelvin, pressure is in atmospheres, and volume should be in liters.