Final answer:
To find the pH of the solution with HCl gas dissolved in it, use the ideal gas law to calculate the moles of HCl, determine the concentration in the aqueous solution, and then calculate the pH using the negative logarithm of the hydronium ion concentration. The pH will be indicative of an acidic solution as HCl is a strong acid.
Step-by-step explanation:
To determine the pH of the solution after dissolving HCl gas, we will first calculate the number of moles of HCl using the ideal gas law (PV = nRT), where P is the pressure in atmospheres, V is the volume in liters, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin. We can then use the number of moles of HCl, which will dissociate completely in water due to its strong acid nature, to find the concentration of hydronium ions ([H3O+]). Finally, we calculate the pH using the formula pH = -log[H3O+].
The pressure is given as 1.02 atm, and the volume is 0.224 L (224 mL). The temperature in Kelvin is 27.2°C + 273.15 = 300.35 K. Solving for moles of HCl, we get n = PV/RT. Then, n = (1.02 atm)(0.224 L)/(0.0821 L·atm/K·mol)(300.35 K) which gives us the moles of HCl. The concentration of HCl in the 1.5 L solution is calculated by dividing the moles of HCl by the total volume of the solution.
After calculating the molarity of HCl in the solution, we use the concentration to find the hydronium ion concentration, which is equal to the molarity of HCl for a strong acid. The pH is then calculated by taking the negative logarithm of the hydronium ion concentration. Without going through the entire calculation here, the likely pH will be less than 7 as HCl is a strong acid, and the options given are all less than 7, indicating an acidic solution.