Question

Assuming ideal solution behavior, how many liters of HCl gas, measured at 30.0 °C and 745 torr, are required to prepare 1.25 L of a 3.20-M solution of hydrochloric acid?

A)10.5 L

B)103.5 L

C) 95.2 L

D) 101.5 L

Answer 1

To prepare a 3.20-M solution of hydrochloric acid, 101.5 liters of HCl gas are required.

Step-by-step explanation:

To determine the number of liters of HCl gas required to prepare a 3.20-M solution, we can use the formula:

HCl (g) + H2O (l) -> H3O+ (aq) + Cl- (aq)

First, we need to calculate the moles of HCl needed:

moles of HCl = volume of solution (L) * concentration of solution (M)

moles of HCl = 1.25 L * 3.20 M = 4.00 mol

Next, we can use the ideal gas law to calculate the volume of HCl gas:

volume of HCl gas = moles of HCl * (RT/P)

where R is the ideal gas constant (0.0821 L·atm/mol·K), T is the temperature in Kelvin, and P is the pressure in atm. Converting the temperature to Kelvin:

T = 30.0 °C + 273.15 = 303.15 K

Using the given pressure:

P = 745 torr / 760 torr/atm = 0.9789 atm

Plugging in the values:

volume of HCl gas = 4.00 mol * (0.0821 L·atm/mol·K * 303.15 K / 0.9789 atm) = 101.49 L

Rounding to the nearest tenth:

The answer is 101.5 L (D).