Question

The EMF of cell: \(\mathrm{H}_{2}(\mathrm{~g}) \mid\) Buffer \(\|\) Normal calomel electrode, is \(0.70 \mathrm{~V}\) at \(25^{\circ} \mathrm{C}\), when barometric pressure is \(760 \mathrm{~mm}\). What is the \(\mathrm{pH}\) of the buffer solution? \(E^{\circ}\). calomel \(=0.28 \mathrm{~V} .[2.303 R T / F=0.06]\) (a) \(3.5\) (b) \(7.0\) (c) tending to zero (d) tending to \(14.0\)

Short answer

The pH of the buffer solution is 7.0

Step-by-step solution

Understanding the Nernst Equation

The EMF of the cell is determined using the Nernst Equation for a hydrogen electrode, which is combined with any other electrode (in this case, the calomel electrode). The equation for the hydrogen electrode when connected to a SHE (Standard Hydrogen Electrode) is: E_cell = E^0_cell - (2.303RT/F) * (pH) where:E_cell is the cell potential under non-standard conditions,E^0_cell is the standard cell potential,R is the universal gas constant,T is the temperature in Kelvin,F is the Faraday's constant,and pH is the negative logarithm of the hydrogen ion concentration.

Insert given values and calculate the pH

Given E_cell = 0.70 V, E^0_calomel = 0.28 V, and 2.303RT/F = 0.06 V at 25 degrees Celsius, we can find pH by rearranging the formula:0.70 = 0.28 - 0.06 * pHNow solve for pH:0.06 * pH = 0.28 - 0.70pH = -(0.70 - 0.28) / 0.06pH = -0.42 / 0.06pH = 7.0

Verify and Choose the Correct Answer

After computation, the pH is found to be 7.0. Look for this value among the given options to choose the correct answer. In this case, option (b) \(7.0\) is the correct answer.

Key concepts

EMF of Electrochemical Cells

Understanding the electromotive force (EMF) of electrochemical cells is crucial for numerous applications in chemistry and technology. EMF is the voltage developed by any source of electrical energy, such as a battery or fuel cell. In the context of chemistry, it is the difference in electrical potential between two electrodes when there is no current flowing. This measurement is critical when analyzing the efficiency and direction of spontaneous reactions within the cell.

When a voltaic or galvanic cell is operational, the EMF represents the driving force that moves electrons from the anode to the cathode through an external circuit. The EMF of a cell under standard conditions is denoted as E° and is measured in volts (V). It can be determined experimentally, or calculated using tables of standard electrode potentials, which reflect the inherent tendency of a species to lose or gain electrons and thus become oxidized or reduced, respectively.

pH Calculation

The pH calculation is a common task in chemistry, involving the determination of the acidity or basicity of a solution. pH is defined as the negative base 10 logarithm of the molar concentration of hydrogen ions in a solution (\( \text{pH} = -\text{log}[H^+] \)). The scale ranges from 0 to 14, with 7 being neutral, values less than 7 indicating acidic conditions, and values above 7 indicating alkaline conditions.

To find the pH, chemists often employ the Nernst equation, which correlates the EMF of a cell with the pH of the solution, especially when working with electrochemical cells involving the hydrogen electrode. Knowledge of the pH is vital in various scientific fields, such as biochemistry, environmental science, and pharmaceuticals, and it influences myriad processes from enzyme activity to water quality analysis.

Standard Hydrogen Electrode

The Standard Hydrogen Electrode (SHE) is a fundamental reference point within electrochemistry. It is used as the zero point for measuring the standard electrode potentials of other electrodes. Composed of a platinum electrode coated with platinum black, the SHE is immersed in an acidic solution and hydrogen gas is bubbled over it at a pressure of 1 atm.

The SHE provides a stable reference, as its potential under standard conditions (25°C, 1 atm pressure, and 1 M concentration) is declared to be 0 volts. In exercises involving the Nernst equation, electrodes are often compared to the SHE to elucidate their potential differences and, consequently, their abilities to drive reactions.

Calomel Electrode

The Calomel Electrode is another type commonly used reference electrode, especially for pH measurements and potentiometric titrations. It consists of mercury and mercury(I) chloride (also known as calomel) submerged in a solution of potassium chloride. The potential of the calomel electrode depends on the concentration of the electrolyte within it and it is known for its stable and well-characterized potential.

When partnered with the SHE in the context of the Nernst equation, the potential established by the calomel electrode (denoted as E°_calomel) is critical. In our specific case, knowing that E°_calomel is 0.28 V allows us to calculate the pH of the buffer solution in combination with the overall EMF of the electrochemical cell. This type of calculation provides an essential understanding of the relationships between electrode potentials, cell EMF, and hydrogen ion concentrations.