The same quantity of electricity is passed through 2voltameters connected in series, one copper voltmeter with copper electrode in a copper(ii) tetraoxosulphate(vi) solution. The other platinum electrode in a dilute solution of tetraoxosulphate (vi) acid. 500cm³ of dry hydrogen gas measured at 20°C and 720mmHg are collected in one voltmeter. What mass of copper will be deposited on the cathode of the other? (Cu=64,H=1,Faraday's constant 96500Cmol-1,molar volume =22.4dm³..
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To calculate the mass of copper that will be deposited on the cathode, we can use Faraday's laws of electrolysis. According to Faraday's first law, the mass of a substance produced at an electrode is directly proportional to the quantity of electricity passed through it.
Now, let's break it down step by step:
1. Determine the quantity of electricity passed through the voltmeter collecting the hydrogen gas. To do this, we need to know the current (I) and the time (t) it took to collect the gas.
2. Use Faraday's law to find the number of moles of hydrogen gas. Since 1 mole of hydrogen gas is equal to 2 moles of electrons, we can determine the number of electrons (n) using the equation n = (I * t) / (2 * Faraday's constant).
3. Calculate the number of moles of copper ions (Cu2+) that will be reduced. According to the balanced chemical equation for the reduction of copper ions, 2 moles of electrons are required to produce 1 mole of copper. So, the number of moles of copper ions (Cu2+) is equal to half the number of moles of electrons.
4. Finally, use the molar mass of copper (Cu) to calculate the mass of copper deposited on the cathode.
Remember to convert units as necessary and keep track of significant figures. Let me know if you need any further assistance!
To determine the mass of copper deposited on the cathode, we need to calculate the number of moles of electrons transferred and then use the stoichiometry to find the corresponding mass of copper.
Step 1: Calculate the number of moles of hydrogen gas collected in the voltmeter.
Using the ideal gas law equation: PV = nRT
where
P = pressure = 720 mmHg
V = volume = 500 cm³ = 0.5 dm³
n = number of moles
R = ideal gas constant = 0.0821 dm³·atm/(mol·K)
T = temperature in Kelvin
Converting temperature from Celsius to Kelvin:
T = 20°C + 273.15 = 293.15 K
Rearranging the equation to solve for n:
n = PV / RT
n = (720 mmHg * 0.5 dm³) / (0.0821 dm³·atm/(mol·K) * 293.15 K)
n = 12.35 mol
Step 2: Calculate the number of moles of electrons transferred.
Since hydrogen gas is being collected in one voltmeter, the number of moles of electrons transferred is equal to the number of moles of hydrogen gas.
Number of moles of electrons transferred = 12.35 mol
Step 3: Calculate the mass of copper deposited on the cathode.
1 mole of electrons transferred corresponds to 1 mole of copper deposited on the cathode.
Using the molar mass of copper (Cu = 64 g/mol):
Mass of copper deposited = number of moles of electrons transferred * molar mass of copper
= 12.35 mol * 64 g/mol
= 790.4 g
Therefore, approximately 790.4 grams of copper will be deposited on the cathode.
To find the mass of copper deposited on the cathode, we can follow these steps:
Step 1: Calculate the number of moles of hydrogen gas collected.
We have the volume (500 cm³), so we need to convert it to cubic decimeters (dm³). Since 1 dm³ is equivalent to 1000 cm³, we divide 500 cm³ by 1000 to get 0.5 dm³.
Given that the molar volume is 22.4 dm³, we divide 0.5 dm³ by 22.4 dm³ to get the number of moles of hydrogen gas collected.
Number of moles of hydrogen gas = 0.5 dm³ / 22.4 dm³ = 0.0223 moles
Step 2: Calculate the number of moles of electrons transferred.
Since hydrogen gas is being collected, we can determine the number of moles of electrons transferred by using the equation for the electrolysis of water:
2H₂ → 4H⁺ + 4e⁻
From the equation, we can see that for every 2 moles of hydrogen gas, 4 moles of electrons are transferred. Therefore, we multiply the number of moles of hydrogen gas by 4:
Number of moles of electrons = 0.0223 moles * 4 = 0.0892 moles
Step 3: Calculate the number of moles of copper deposited.
According to Faraday's law, 1 mole of electrons is required to deposit 1 mole of copper. Therefore, the number of moles of copper deposited is also 0.0892 moles.
Step 4: Calculate the mass of copper deposited.
The molar mass of copper is 64 g/mol (as given). To find the mass of copper deposited, we multiply the number of moles of copper by the molar mass of copper:
Mass of copper deposited = 0.0892 moles * 64 g/mol = 5.7088 g
Therefore, approximately 5.71 grams of copper will be deposited on the cathode.