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An electric current is passed through silver voltameter connected to a water voltameter. The cathode of the silver voltameter weighed \(0.108 \mathrm{~g}\). more at the end of the electrolysis. The volume of oxygen evolved at STP is a. \(5.6 \mathrm{~cm}^{3}\) b. \(56 \mathrm{~cm}^{3}\) c. \(11.2 \mathrm{~cm}^{3}\) d. \(560 \mathrm{~cm}^{3}\) e. \(22.4 \mathrm{~cm}^{3}\)

Short Answer

Expert verified
The volume of oxygen evolved at STP is 5.6 cm³.

Step by step solution

01

Use Faraday's Laws of Electrolysis

According to Faraday's first law of electrolysis, the mass of the substance deposited (or dissolved) at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. For silver, the amount of silver deposited is given as 0.108 g.
02

Calculate the Equivalent Weight of Silver

The equivalent weight of silver is calculated using the atomic mass and valency since it has one positive charge. Silver's atomic mass is 108 g/mol, hence its equivalent weight is also 108 g/equiv.
03

Determine the Quantity of Electricity Passed

Using the formula \( W = \frac{Q}{96500} \times E_w \), where \( W \) is the weight deposited, \( Q \) is the quantity of electricity, and \( E_w \) is the equivalent weight. Rearranging gives \( Q = \frac{W \times 96500}{E_w} = \frac{0.108 \times 96500}{108} = 96.5 \, \text{Coulombs} \).
04

Relate Oxygen Evolution to Electricity

In a water voltameter, the electrolysis of water splits it into hydrogen and oxygen gases. The amount of oxygen produced (O\(_2\)) is directly proportional to the quantity of electricity. From Step 3, we found that 96.5 Coulombs is passed. Since 4 Faradays are required to liberate 1 mole of O\(_2\), we need to calculate the volume of O\(_2\).
05

Calculate Volume of Oxygen at STP

First, determine the moles of O\(_2\) produced using \( \text{mole O}_2 = \frac{Q}{4 \times 96500} = \frac{96.5}{386000} \approx 0.00025 \. \). The volume of 1 mole of gas at STP is 22400 cm³, so \( \text{Volume O}_2 = 0.00025 \times 22400 = 5.6 \, \text{cm}^3 \).
06

Choose the Correct Answer

Based on our calculation, the volume of oxygen evolved at STP is found to be 5.6 cm³, which matches option (a).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrolysis
Electrolysis is a fascinating chemical process that involves passing an electric current through an electrolyte to cause a chemical change. This method is commonly used to separate elements from their naturally occurring sources, such as ores, using an electric current. In simple terms, electrolysis involves the movement of electrons in a solution leading to chemical reactions. These reactions occur at the electrodes submerged in the electrolyte.

The process occurs as follows:
  • The electrolyte is broken down into ions, which are attracted towards oppositely charged electrodes.
  • Cations (positively charged ions) move towards the cathode (negative electrode) and gain electrons (reduction).
  • Anions (negatively charged ions) move towards the anode (positive electrode) and lose electrons (oxidation).
  • This movement of ions causes a chemical change, leading to the deposition or dissolution of substances at the electrodes.
Faraday's Laws of Electrolysis govern these processes, stating how the quantity of electricity affects the amount of substance changed. The mass of the substance deposited or liberated is directly proportional to the total electric charge passed. Understanding electrolysis is key to grasping various industrial processes like electroplating and the extraction of metals.
Equivalent Weight
When studying chemical changes in electrolysis, its important to understand the concept of equivalent weight. Equivalent weight refers to the measure of a substance's ability to react with or displace another substance. This is a critically important concept in electrolysis, determining how much of a substance will be deposited or dissolved during the process. It is calculated as follows:

  • Take the atomic or molecular weight of a substance.
  • Divide it by the valency (or the number of electrons gained or lost) of the substance.

For example, in the case of silver, the atomic mass is 108 g/mol, and since it loses one electron (one positive charge), its equivalent weight is 108 g/equiv.

Equivalent weight helps in calculating the amount of a substance that will be deposited during electrolysis when a certain quantity of electricity is passed. It's essential in determining the precise conditions needed for industrial electrochemical processes.
STP (Standard Temperature and Pressure)
In the context of gases and their behavior, Standard Temperature and Pressure (STP) is a commonly used reference point. It helps scientists and engineers compare gases under consistent conditions, which is pivotal for calculations in electrolysis.

STP is defined by:
  • Temperature: 273.15 Kelvin (0°C)
  • Pressure: 1 atmosphere (101.325 kPa)

At these conditions, one mole of an ideal gas occupies 22.4 liters or 22,400 cubic centimeters. Understanding STP is crucial when dealing with electrolysis, especially when calculating the volumes of gases produced or consumed, such as the oxygen evolved in a water voltameter.

Calculating the volume of gases at STP allows for accurate comparisons and helps predict the outcomes of a reaction under these conditions. For instance, in our example exercise, knowing the volume that one mole of oxygen gas occupies at STP is necessary to calculate the exact amount produced during the process. Such calculations are not only textbook exercises but also have real-world applications in chemical manufacturing and industrial processes.

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Most popular questions from this chapter

How many moles of electrons, are transferred in the following reduction- oxidation reaction? \(2 \mathrm{MnO}_{4}^{-}(\mathrm{aq})+16 \mathrm{H}^{+}(\mathrm{aq})+10 \mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow\) $$ 2 \mathrm{Mn}^{2+}(\mathrm{aq})+5 \mathrm{Cl}_{2}(\mathrm{~g})+8 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) ? $$ a. 2 b. 5 c. 10 d. 12

Electrolysis of water gives \(11.2 \mathrm{~L}\) of hydrogen at STP at the cathode. The oxygen evolved at the anode under similar conditions is a. \(5.6 \mathrm{~L}\) b. \(11.2 \mathrm{~L}\) c. \(0.25 \mathrm{~mol}\) d. \(8 \mathrm{~g}\)

A standard hydrogen electrode has zero electrode potential because a. hydrogen is easiest to oxidize b. this electrode potential is assumed to be zero c. hydrogen atom has only one electron d. hydrogen is the lightest element

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