A 19.9mL volume of a hydrochloric acid solution reacts completely with a solid sample of magnesium carbonate, producing 183mL of CO2 that is collected over water at 24.0 degrees C and 738 torr total pressure. The vapor pressure for water at 24.0 degrees C is 22.39 mmHg. What is the molarity of the hydrochloric acid solution?
MgCO3 + 2HCl ==> H2) + CO2 + MgCl2
Use PV = nRT to correct 183 mL CO2 at the conditions listed to STP You want to solve for n = number of mols CO2. Note that P = (738-22.39)/760 = ? atm.
mols CO2 @ STP/2 = mols HCl
M HCl = mols HCl/L HCl
To find the molarity of the hydrochloric acid solution, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in this case, CO2)
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the pressure of the CO2 from torr to atm:
Total pressure = P(CO2) + P(H2O vapor)
738 torr = P(CO2) + 22.39 mmHg
Converting the water vapor pressure to atm:
22.39 mmHg * (1 atm / 760 mmHg) = 0.0295 atm
Now we can solve for P(CO2):
738 torr - 0.0295 atm = P(CO2)
708.71 torr = P(CO2)
Next, we need to convert the volumes of CO2 and HCl to liters. We can use the conversion factor:
1 mL = 0.001 L
Volume of CO2 collected over water:
183 mL * 0.001 L/mL = 0.183 L
Volume of the hydrochloric acid solution:
19.9 mL * 0.001 L/mL = 0.0199 L
Now, let's convert the temperature to Kelvin:
24.0 degrees C + 273.15 = 297.15 K
The ideal gas constant, R, is equal to 0.0821 L·atm/(mol·K).
Now we have all the values we need to solve for the number of moles of CO2 using the ideal gas law:
(P(CO2) * V) = (n * R * T)
(708.71 torr * 0.183 L) = (n * 0.0821 L·atm/(mol·K) * 297.15 K)
129.7593 = (n * 24.389415)
129.7593 / 24.389415 = n
n ≈ 5.32 mol
Since the reaction between 1 mole of hydrochloric acid and 1 mole of magnesium carbonate produces 1 mole of CO2, the number of moles of HCl is also 5.32 mol.
To find the molarity, we divide the number of moles of HCl by the volume of HCl in liters:
Molarity (M) = (moles of solute) / (volume of solution in liters)
Molarity of HCl solution = 5.32 mol / 0.0199 L
Molarity of HCl solution ≈ 267.34 M (rounded to two decimal places)
Therefore, the molarity of the hydrochloric acid solution is approximately 267.34 M.
To find the molarity of the hydrochloric acid solution, we need to use the volume of the acid and the stoichiometry of the reaction.
First, let's find the number of moles of hydrogen chloride (HCl) used in the reaction. We know that the volume of the acid solution is 19.9 mL, and we can assume that the solution is aqueous (in water). However, the volume of CO2 produced is given at standard temperature and pressure (STP), which is 0 degrees Celsius and 1 atmosphere (atm) pressure.
To convert the volume of CO2 at STP to the volume at the given conditions, we can use the ideal gas law equation: PV = nRT.
n = PV / RT,
where P is the pressure, V is the volume, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is the temperature in Kelvin.
First, we need to convert the pressure given in torr to atm:
738 torr * (1 atm / 760 torr) ≈ 0.971 atm.
Next, let's convert the temperature from degrees Celsius to Kelvin:
24.0 degrees Celsius + 273.15 = 297.15 K.
Now we can calculate the volume of CO2 at the given conditions:
V = (183 mL) * (0.971 atm) * (297.15 K) / (1 atm) * (273.15 K) = 169.7 mL.
Now that we have the volume of CO2 at the given conditions, let's convert it to liters:
169.7 mL * (1 L / 1000 mL) = 0.1697 L.
The balanced equation for the reaction between hydrochloric acid (HCl) and magnesium carbonate (MgCO3) is:
2 HCl(aq) + MgCO3(s) → MgCl2(aq) + CO2(g) + H2O(l).
From the equation, we see that 2 moles of HCl react with 1 mole of CO2. Therefore, the moles of HCl can be calculated by:
moles of HCl = 0.1697 L CO2 * (2 mol HCl / 1 mol CO2) = 0.3394 mol HCl.
Finally, we can calculate the molarity (M) of the HCl solution using the volume of the acid solution:
Molarity of HCl = moles of HCl / volume of HCl solution in liters,
Molarity of HCl = 0.3394 mol / (19.9 mL * (1 L / 1000 mL)) = 17.04 M.
Therefore, the molarity of the hydrochloric acid solution is approximately 17.04 M.