An unknown metal M forms a soluble compound, M(NO3)2. A solution of M(NO3)2 is electrolyzed. When a constant current of 2.5 amperes is applied for 35 minutes, 3.06 grams of the metal M is deposited. Calculate the molar mass of M and identify the metal.
To calculate the molar mass of metal M, we need to use the equation:
Molar mass = (Amount of substance) / (Number of moles)
First, let's calculate the number of moles of metal M deposited using the formula:
Number of moles = (Amount of substance) / (Molar mass)
From the given information, we know that 3.06 grams of metal M is deposited. We also know that the amount of substance is equal to the number of moles.
Therefore, the number of moles of metal M is:
Number of moles = 3.06 grams / (molar mass of M)
We are given that a constant current of 2.5 amperes is applied for 35 minutes. To convert minutes to hours, divide 35 minutes by 60:
Time = 35 minutes / 60 = 0.58 hours
Now, we can use Faraday's law of electrolysis:
Amount of substance = (Current × Time) / (Faraday's constant)
Plugging in the values we have:
3.06 grams = (2.5 amperes × 0.58 hours) / (Faraday's constant)
To find the molar mass, we need to know Faraday's constant. Faraday's constant is the charge per mole of electrons passing through a mole of electrons, equal to 96,487 coulombs.
Plugging in this value:
3.06 grams = (2.5 amperes × 0.58 hours) / 96487 C
Now, let's solve for the molar mass:
(2.5 amperes × 0.58 hours) / (96487 C) = 3.06 grams / (molar mass of M)
Cross-multiplying:
(molar mass of M) × (2.5 amperes × 0.58 hours × 96487 C) = 3.06 grams
Simplifying:
(molar mass of M) = (3.06 grams) / (2.5 amperes × 0.58 hours × 96487 C)
Calculating the final value will give us the molar mass of metal M.
To determine the molar mass and identify the metal M, we can use Faraday's law of electrolysis. According to Faraday’s first law, the amount of substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.
First, let's calculate the charge passed through the electrolyte using the formula:
Q (coulombs) = I (amperes) x t (time in seconds)
Since the time is given in minutes, we need to convert it to seconds:
35 minutes = 35 minutes x 60 seconds/minute = 2100 seconds
Now, we can calculate the charge passed:
Q = 2.5 A x 2100 s
Q = 5250 C
Next, we need to convert the charge into moles using Faraday's constant (F). The value of Faraday's constant is 96500 C/mol.
n (moles) = Q (Coulombs) / F (Coulombs per mole)
n = 5250 C / 96500 C/mol
n ≈ 0.054 moles
Since 3.06 grams of metal M is deposited, we can calculate the molar mass using the formula:
Molar Mass (g/mol) = Mass (g) / Moles (moles)
Molar Mass = 3.06 g / 0.054 mol
Molar Mass ≈ 56.67 g/mol
Finally, we need to identify the metal with this molar mass. By checking the periodic table, we find that the closest molar mass to 56.67 g/mol is that of Barium (Ba) with a molar mass of 137.33 g/mol.
Therefore, the metal M is Barium (Ba) with a molar mass of approximately 137.33 g/mol.
113 g/mole
CD is the metal