What is [H30+] in a solution obtained by dissolving 205mL HCl(g), measured at 23 C and 751mmHg, in 4.25L of aqueous solution?

Use PV = nRT to determine n = number of moles HCl at that T and P. Then M = moles/L soln.

Thanks so much. I did that and I used 751 for P, .205L for V, 0.08206 for R and 296 K for T and I got 6.34 moles. When I substituted that into the formula for M = moles/L I got 30.9 but the actual answer that is written in my textbook is 1.96 x 10^-3 M.

To find the concentration of [H30+] in the solution, we need to calculate the moles of HCl gas dissolved and then determine the concentration of [H30+].

Step 1: Convert the volume of HCl gas to moles.
Given:
Volume of HCl gas = 205 mL
Temperature = 23°C
Pressure = 751 mmHg

First, we need to convert the temperature to Kelvin:
Temperature(K) = Temperature(°C) + 273.15
Temperature(K) = 23°C + 273.15 = 296.15 K

Next, we need to convert the pressure from mmHg to atm:
Pressure(atm) = Pressure(mmHg) / 760
Pressure(atm) = 751 mmHg / 760 = 0.9882 atm

Now, we can calculate the moles of HCl gas using the ideal gas law equation:
PV = nRT

n = (PV) / (RT)
where:
n = moles of gas
P = pressure (in atm)
V = volume (in liters)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)

Volume of HCl gas (in liters) = Volume of HCl gas (in mL) / 1000
Volume of HCl gas = 205 mL / 1000 = 0.205 L

Now, we can compute the moles of HCl gas:
n = (0.9882 atm * 0.205 L) / (0.0821 L·atm/(mol·K) * 296.15 K)

Note: We convert the volume from mL to L because the value of R is given in liters and not milliliters.

Step 2: Calculate the concentration of [H30+].
The stoichiometry of HCl (hydrochloric acid) dissociation in water is 1:1, so the concentration of [H3O+] is equal to the concentration of HCl.

Given:
Volume of aqueous solution = 4.25 L

Concentration of [H3O+] = (moles of HCl) / Volume of solution
Concentration of [H3O+] = (moles of HCl) / (4.25 L)

Finally, substitute the calculated value of moles of HCl gas and find the concentration of [H3O+].

Note: The calculated concentration would depend on the value of moles of HCl gas and the given volume of the solution. You can perform the final calculation using the obtained values to find the concentration of [H3O+].