A 0.069 gram sample of a metal reacted with HCl and produced 45.31 mL of H
2
gas at
25¡ÆC and 1 atm pressure. The metal is known to react with HCl according to the following
reaction,
2 M + 6 HCl
> 2 MCl
3
+ 3 H
2
What is the molar mass of the metal? Which metal is it?
You would do better to write your equations in a left to right line (horizontal) rather than a vertical line.
2M + 6HCl>>> 2MCl3 + 3H2
Use PV = nRT and solve for n H2 gas.
Using the coefficients in the balanced equation, convert mols H2 to mols M. Then mols = grams/molar mass. You know grams and mols, solve for molar mass.
Then identify the element from the periodic table.
NOTE: This metal actually forms MCl2 with HCl and not MCl3.
To find the molar mass of the metal and determine which metal it is, we can use the given information and apply the concept of stoichiometry.
First, let's calculate the number of moles of H2 gas produced.
Given:
Mass of the metal sample (m) = 0.069 grams
Volume of H2 gas (V) = 45.31 mL = 0.04531 L (converted to liters)
Temperature (T) = 25°C (converted to Kelvin by adding 273.15) = 298.15 K
Pressure (P) = 1 atm
Using the ideal gas law equation PV = nRT, where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature
Rearranging the equation, we can solve for the number of moles (n) of H2 gas:
n = PV / RT
Substituting the given values:
n = (1 atm) * (0.04531 L) / (0.0821 L·atm/(mol·K)) * (298.15 K)
Calculating the value of n, we get:
n ≈ 0.002 moles
Now, let's use the balanced chemical equation to find the number of moles of the metal.
According to the balanced equation:
2 M + 6 HCl -> 2 MCl3 + 3 H2
From the equation, we can see that 2 moles of the metal react to produce 3 moles of H2.
Setting up a ratio:
2 moles of the metal / 3 moles of H2 = x moles of the metal / 0.002 moles of H2
Solving for x, the number of moles of the metal, we get:
x ≈ (2 moles / 3 moles) * 0.002 moles
x ≈ 0.001333 moles
Now that we know the number of moles of the metal, we can calculate the molar mass.
Molar mass (M) = mass (m) / moles (n)
M = 0.069 grams / 0.001333 moles
Calculating the molar mass, we get:
M ≈ 51.78 g/mol
So the molar mass of the metal is approximately 51.78 g/mol.
To determine which metal it is, we need to compare the molar mass calculated with the molar masses of known elements. By searching a periodic table or reference source, we find that the element with a molar mass closest to 51.78 g/mol is Antimony (Sb).
Therefore, the metal in question is most likely Antimony (Sb).