A 0.464 gram sample of a metal, M, reacts completely with sulfuric acid according to:
M(s) +H2SO4(aq)=MSO4(aq)+H2(g)
A volume of 211 mL of hydrogen is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 756.0 Torr and the temperature is 25°C. Calculate the atomic mass of the metal. Every time it's wrong. Please walk me through this
I think there must be a correction for the vapor pressure of H2O at the temperature stated.
That would make that part
(756-23.8)(0.211)/[(62.364*298)]= 0.00831 mols. Then proceed to molar mass.
Okay, I think I see why.
Sure! Let's go step by step to solve this problem.
1. First, we need to find the number of moles of hydrogen gas collected. To do that, we can use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
Since we are collecting the gas over water, we need to consider the vapor pressure of water at the given temperature. At 25°C, the vapor pressure of water is 23.8 Torr. So the pressure of just the hydrogen gas is the total pressure (756.0 Torr) minus the vapor pressure of water (23.8 Torr), which equals 732.2 Torr.
Converting the pressure from Torr to atm, we get 732.2 Torr / 760 Torr/atm = 0.963 atm.
Now, plugging the values into the ideal gas law equation, we have (0.963 atm) * (0.211 L) = n * (0.0821 L·atm/(mol·K)) * (298 K). Solving for n, we find n = 0.01035 moles of hydrogen gas.
2. Next, we need to determine the mole ratio between the metal (M) and the hydrogen gas (H2) using the balanced chemical equation. From the equation provided, we can see that one mole of metal reacts with one mole of hydrogen gas. Therefore, the number of moles of metal (M) equals the number of moles of hydrogen gas, which is 0.01035 moles.
3. Now, we can calculate the molar mass of the metal (M). We are given that the mass of the metal sample is 0.464 grams.
Using the equation: molar mass = mass / moles, we can divide 0.464 grams by 0.01035 moles to find the molar mass of the metal. The result is approximately 44.9 grams/mol.
Therefore, the atomic mass of the metal is approximately 44.9 grams/mol.
To calculate the atomic mass of the metal (M), we need to find the number of moles of hydrogen gas (H2) produced in the reaction. From there, we can use the stoichiometry of the reaction to determine the molar ratio between M and H2 and then calculate the atomic mass of M.
Step 1: Convert the volume of hydrogen gas to the number of moles.
From the ideal gas law, we can use the following equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
We need to convert the pressure and volume to the appropriate units before plugging them into the equation.
Since the pressure is given in Torr and the temperature is in Celsius, we need to convert them:
- Convert 756.0 Torr to atm: 756.0 Torr ÷ 760 Torr/atm = 0.9947 atm
- Convert 25°C to Kelvin: 25°C + 273.15 = 298.15 K
Now we can calculate the number of moles of hydrogen gas:
n = (PV) / (RT)
n = (0.9947 atm * 0.211 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
Step 2: Calculate the moles of M based on the stoichiometry of the reaction.
From the balanced chemical equation, we can see that the molar ratio between M and H2 is 1:1. This means that the moles of hydrogen gas produced are equal to the moles of metal M.
Step 3: Calculate the atomic mass of the metal.
The atomic mass of a substance is calculated by dividing the mass of the substance by the number of moles:
Atomic mass = mass / moles
We are given that the mass of the metal sample is 0.464 grams. Divide this mass by the moles calculated in step 2 to obtain the atomic mass of the metal.
Please note that the calculation provided is a general guideline. It is best to always double-check your conversion factors and ensure proper unit conversions to get an accurate result.
R=62.3637 L·Torr/mol·K
L=0.211L
P=756.0 Torr
T=273.15+25ºC
Use PV=nRT and solve for moles, n.
moles of H2=n=PV/RT
moles of H2=moles of M
You know that
moles of M=0.464g of M
and
1 mole of M=Atomic weight
(moles of M/0.464g of M)=(1 mole of M/Atomic weight)
solve for atomic weight,
atomic weight=0.464g of M/moles of M