Question

An alloy of silver and gold contains 38.5% silver by mass and has a density of $14.6\,g\,m{{L}^{-1}}$. What is the molar concentration of silver in this alloy?
A.\[52.04mol{{L}^{-1}}\]
B.\[45.6\,mol{{L}^{-1}}\]
C.\[3.5\,7\,mol{{L}^{-1}}\]
D.\[2.64\,mol{{L}^{-1}}\]

Answer 1

Hint: To calculate the molar concentration, we should first calculate the mass of silver in 100 gram of alloy. After that we will calculate, volume of the solution by using density.

Step by step answer:
To answer this question, we should know to find molar concentration. To find molar concentration of silver in alloy we need moles of Ag and volume of solution.
To find moles moles of Ag, we require mass of the silver that is mixed to form alloy. In this question we have given that, alloy of silver and gold contains 38.5% of silver. So, if we take a total 100 gram of alloy, then 38.5% of silver in this 100 gram alloy is 38.5 gram.
So, mass of silver is = 38.5 gram
Molar mass of silver= 107.86 gram per mole.
Number of moles of silver= $\dfrac{mass\,of\,silver}{Molar\,mass\,of\,silver}=\dfrac{38.5}{107.86}=0.35$mole
Moles of solute that is required to find molar concentration of silver is 0.35 moles.
Now, in the next part we now require a volume of solution.
As given in the question, the density of gold and silver alloy is 14.6 gram per millilitre.
In calculation of numbers of mole, we had calculated the mass of the alloy to be 100 gram.
So, by using density formula:
$\begin{align}
  & Density=\dfrac{mass}{volume} \\
 & volume\,of\,solution=\dfrac{mass}{density} \\
 & volume\,of\,solution=\dfrac{100\,gram}{14.6\dfrac{gram}{ml}}\to 6.84ml \\
 & \\
\end{align}$
Now, we have both moles of solute and volume of solution to calculate molar concentration.

\[\begin{align}
  & Molar\,concentration(molarity)=\dfrac{Moles\,\,of\,solute}{Volume\,of\,solution(in\,Litres)} \\
 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\dfrac{0.35\,moles}{\dfrac{6.84}{1000}L}\to 52.04mol{{L}^{-1}} \\
\end{align}\]
So, the answer to this question is option A. We have successfully calculated molar concentration of silver in alloy gold and silver and that is \[52.04mol{{L}^{-1}}\].

Note: We should know that molarity or molar concentration is the number of moles of solute per litre of solution. We use this unit for stoichiometric calculations to determine the amount of chemical in a given mixture. We should not confuse moles with molarity: molarity is a measure of concentration, while moles are a measure of the amount of substance. We should know that stoichiometry deals with the relative quantities of reactants and products in chemical reactions. It can be used to find the quantities of the products from given reactants in a balanced chemical reaction, as well as percent yield.