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The same amount of charge that liberated 2.158 gm of silver was passed through a solution of gold salt, where 1.314 gm of gold was deposited. Find the equivalent mass of gold and valency of gold.

Last updated date: 13th Jun 2024
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Hint: To determine the equivalent mass of gold, relation between equivalent weight and mass can be applied, as mass of gold, mass of silver and equivalent mass of valency are given. By calculating the equivalent mass of gold we can determine its valency by using the formula for calculating the equivalent weight.

Complete step by step answer:
The mass of silver (Ag) is 2.158 gm.
The mass of gold (Au) is 1.314 gm.
The equivalent mass of silver (Ag) is 107.9
The formula to calculate the equivalent mass of gold (Au) is shown below.
$\dfrac{{{m_1}}}{{{m_2}}} = \dfrac{{{E_1}}}{{{E_2}}}$
${m_1}$ is mass of silver.
${m_2}$ is mass of gold.
${E_1}$ is equivalent mass of silver.
${E_2}$ is equivalent mass of gold.
To determine the value of equivalent mass of gold, substitute the values in the above equation.\[\dfrac{{2.158}}{{1.314}} = \dfrac{{107.9}}{{{E_2}}}\]
\[\Rightarrow {E_2} = \dfrac{{107.9 \times 1.314}}{{2.158}}\]
\[\Rightarrow {E_2} = 65.7\]
Therefore, the equivalent weight of gold (Au) is 65.7.
The equivalent mass is calculated by dividing the atomic mass by the valency.
The formula for equivalent mass is shown below.
\[Eq.wt = \dfrac{{Atomic\; Mass}}{{valency}}\]
From the above formula of equivalent mass, the formula for calculating the valency can be determined as shown below.
\[Valency = \dfrac{{Atomic\; Mass}}{{Eq.wt}}\]
The atomic mass of gold is 197.
For calculating the valency, substitute the value of atomic mass of gold and equivalent mass in above equation.
$Valency = \dfrac{{197}}{{65.7}}$
\[\Rightarrow Valency = 3\]

Therefore, the valency of gold is 3.

Note: When the mass of the chemical compound is g grams, then the mass which contain the gram equivalent is given by the formula as shown below.
$g.eq = valency\; factor \times moles$
Gram equivalent weight is the same as the mass present in grams which numerically equal to the equivalent weight.