(1) 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..
(2) A metal of RAM 27 was deposited by electrolysis. If 0.176g of the metal was deposited on the cathode when a current of 0.15A flows for 7/2 hours, what's the charge on the cathode of this metal? (Faraday's constant =96500Cmol-1)...
(1) To find the mass of copper deposited on the cathode, we can use Faraday's law of electrolysis. According to Faraday's law, the mass of a substance deposited or liberated during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.
First, we need to calculate the quantity of electricity passed through the electrolyte. The equation to calculate the quantity of electricity is:
Quantity of electricity (Q) = Current (I) × Time (t)
Given:
Current (I) = 500 cm³ of dry hydrogen gas measured at 20°C and 720 mmHg
Time (t) = Not given
However, we are missing the time (t) component in the given information. Without the time, we cannot calculate the quantity of electricity passed through the electrolyte. Please provide the value of time (t) in order to proceed with the calculation.
(2) To find the charge on the cathode, we can use Faraday's law of electrolysis.
The equation to calculate the charge is:
Charge (Q) = Current (I) × Time (t)
Given:
Current (I) = 0.15 A
Time (t) = 7/2 hours
Before we proceed with the calculation, let's convert 7/2 hours to seconds:
7/2 hours = (7/2) × 3600 seconds
= 12600 seconds
Now, we can calculate the charge:
Charge (Q) = 0.15 A × 12600 seconds
Next, let's use Faraday's constant to convert the charge from Coulombs to moles:
1 Faraday = 96500 C/mol
To find the moles of the metal deposited, we divide the charge by Faraday's constant:
Moles = Charge (Q) / Faraday's constant
Finally, we can use the molar mass of the metal (RAM) to find the mass of the metal deposited:
Mass = Moles × Molar mass
Given:
RAM (Relative Atomic Mass) = 27 g/mol
Charge (Q) = 0.15 A × 12600 seconds
Now, substitute the values into the equation to find the mass of the metal deposited on the cathode.
To answer these questions, we will use the concepts of Faraday's laws of electrolysis and the equations related to electrolysis. Let's break down each question step by step.
(1) The first question involves the deposition of copper on the cathode in one voltmeter and asks for the mass of copper deposited on the cathode of the other voltmeter.
We can start by using Faraday's laws of electrolysis. According to Faraday's first law, the amount of substance deposited on an electrode is directly proportional to the quantity of electricity passed through the electrolyte. The formula for this is:
Mass of substance deposited = (Current × Time × Atomic mass) / Charge on the ion
In this case, the substance being deposited is copper (Cu). The current is the same for both voltmeters since they are connected in series. So, we can use the given current.
Given data:
- Current (I) = 500 cm³ of dry hydrogen gas collected (volume is not relevant here)
- Temperature (T) = 20°C
- Pressure (P) = 720 mmHg
First, we need to calculate the quantity of electricity passed through the electrolyte. To calculate this, we can use the formula:
Quantity of electricity (Q) = Current (I) × Time (t)
Now, let's convert the volume of the gas collected into moles using the ideal gas law equation:
PV = nRT
Where:
- P = Pressure (in Pa)
- V = Volume (in m³)
- n = Number of moles
- R = Ideal gas constant (in J/mol·K)
- T = Temperature (in K)
Before we can use the equation, we need to convert the given pressure and temperature to SI units:
Pressure (P) = 720 mmHg = 720 * 133.322 Pa
Temperature (T) = 20°C = 20 + 273.15 K
Now we can calculate the number of moles using the ideal gas law equation. We'll use the molar volume of an ideal gas to convert the volume from cm³ to m³.
Molar volume = 22.4 dm³/mol = 22.4 * 10⁻³ m³/mol
Number of moles (n) = (Pressure * Volume) / (R * Temperature)
Next, we can calculate the quantity of electricity passed using the current and time given:
Quantity of electricity (Q) = Current (I) × Time (t)
Now, we can substitute the values into the formula for the mass of substance deposited:
Mass of copper deposited = (Quantity of electricity * Atomic mass of copper) / Charge on the copper ion
Atomic mass of copper (Cu) = 64 g/mol
Charge on the copper ion = 2 (from the copper(ii) tetraoxosulphate(vi) solution)
Substitute the values into the formula to find the mass of copper deposited on the other cathode.
(2) The second question involves the deposition of a metal with a relative atomic mass (RAM) of 27 and asks for the charge on the cathode.
The formula to calculate the charge on the cathode is given by the formula:
Charge (Q) = Current (I) × Time (t)
Given data:
- Current (I) = 0.15 A
- Time (t) = 7/2 hours
Substitute the values into the formula to find the charge on the cathode of the metal.
Please note that in both cases, you need to make sure to convert the units to SI units (e.g., meters, seconds, Coulombs, etc.) before substituting them into the formulas to get the correct answers.