Need help solving this problem.
A 0.188g sample of unknown metal, X (s), produced 71.4ml of hydrogen gas when reacted with HCl according to the equation:
X(s)+2HCl(aq)--> XCl2(aq)+H2(g)
The gas was collected over water at 23 degrees C. The levels of water inside and outside the gas collecting tube are identical. The vapor pressure of water at 23 degrees C is 21.1mm Hg and the atmospheric pressure is 752 mm Hg. Calculate the molar mass of the unknown metal, X. (R=0.0821Latm/molK)
I got 1.52 x 10^-4 g/mol as my answer. Professor told me it was wrong... Didn't give me the correct answer and told me to keep trying... No assiatance whatsoever. I have been trying all weekend. What am I doing wrong?
You must find the number of moles in the 0.188 g sample.
How many moles H2 were collected.
PV = nRT
P = (752-21.1)/760 which may be one place you are going wrong. This will be the pressure of the dry hydrogen gas in atm.
V = 71.4 mL (convert to L)
n = solve for this
R = 0.08206
T = 23 C converted to K.
Then look at the equation. moles X will be 1/2 moles H2.
Finally, n = grams/molar mass. YOu know n and grams, solve for molar (atomic) mass. My best guess is Cs
After finding the moles of H2, do the mole ratio between H2 and X in the equation.
After that you have the grams of X and moles of X divide the grams by the moles and you will find the molar mass.
To solve this problem, you need to use the ideal gas law to find the number of moles of hydrogen gas produced, and then use stoichiometry to relate it to the moles of unknown metal X.
Let's start by finding the number of moles of hydrogen gas produced:
1. Calculate the partial pressure of the hydrogen gas:
The total pressure is given as 752 mmHg, and the vapor pressure of water at 23°C is 21.1 mmHg. Therefore, the partial pressure of the hydrogen gas is:
Partial Pressure of H2 = Total Pressure - Vapor Pressure of Water
Partial Pressure of H2 = 752 mmHg - 21.1 mmHg
Partial Pressure of H2 = 730.9 mmHg
2. Convert the partial pressure of hydrogen gas to atmospheres:
1 atm = 760 mmHg, so the partial pressure of hydrogen gas in atm is:
Partial Pressure of H2 (atm) = 730.9 mmHg / 760 mmHg/atm
Partial Pressure of H2 (atm) ≈ 0.960 atm
3. Convert the volume of hydrogen gas to liters:
The volume of hydrogen gas produced is given as 71.4 mL. To convert it to liters, divide by 1000:
Volume of H2 (L) = 71.4 mL / 1000 mL/L
Volume of H2 (L) = 0.0714 L
4. Apply the ideal gas law to find the moles of hydrogen gas:
The ideal gas law is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Rearranging the formula to solve for n, we get:
n = PV / RT
n = (Partial Pressure of H2) * (Volume of H2) / (R * Temperature in Kelvin)
n = (0.960 atm) * (0.0714 L) / (0.0821 L⋅atm/(mol⋅K) * (273.15 + 23) K)
n ≈ 0.0042 mol
Now that we have the moles of hydrogen gas, we can use the stoichiometry of the balanced chemical equation to relate it to the moles of unknown metal X.
From the equation: X(s) + 2HCl(aq) --> XCl2(aq) + H2(g)
We can see that 2 moles of HCl are needed to produce 1 mole of H2.
So, moles of X = (0.0042 mol H2) / 2 = 0.0021 mol
Finally, to calculate the molar mass of unknown metal X, divide the mass of the metal (0.188 g) by the moles (0.0021 mol):
Molar mass of X = Mass of X / Moles of X
Molar mass of X = 0.188 g / 0.0021 mol
Molar mass of X ≈ 89.5 g/mol
Therefore, the molar mass of the unknown metal X is approximately 89.5 g/mol, not 1.52 x 10^(-4) g/mol as you initially obtained. Make sure to check your calculations and units to find any errors.
To solve this problem, we need to use the concept of the ideal gas law and the concept of partial pressure.
The ideal gas law is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
In this problem, we are given the volume of hydrogen gas produced (71.4 ml) and the temperature (23 degrees C, which is 296 K). We also need to account for the vapor pressure of water in the gas collected over water to determine the pressure of the hydrogen gas.
To calculate the pressure of the hydrogen gas, we need to subtract the vapor pressure of water from the atmospheric pressure. The vapor pressure of water at 23 degrees C is given as 21.1 mm Hg. Therefore, the pressure of the hydrogen gas is 752 mm Hg - 21.1 mm Hg = 730.9 mm Hg.
Now we can use the ideal gas law to calculate the number of moles of hydrogen gas produced.
PV = nRT
n = (PV) / (RT)
n = (730.9 mm Hg) * (0.0714 L) / (0.0821 L*atm/mol*K * 296 K)
n = 0.0202 moles of H2 gas
According to the balanced chemical equation, the ratio of moles of X(s) to moles of H2 gas is 1:1. Therefore, the number of moles of X(s) is also 0.0202 moles.
Now, we can calculate the molar mass of X using the given mass of the unknown metal (0.188g) and the number of moles of X.
molar mass = mass / moles
molar mass = 0.188 g / 0.0202 moles
molar mass = 9.3 g/mol
Therefore, the molar mass of the unknown metal X is 9.3 g/mol.
If you obtained a different answer (1.52 x 10^-4 g/mol), there might be an error in your calculations. Please double-check your calculations using the provided steps and ensure that all the given values are correctly accounted for.