Question

An alloy of iron\[\left( {54.7\% } \right)\], nickel $\left( {45\% } \right)$and manganese $\left( {0.3\% } \right)$has a density of$8.17g/c{m^3}$. How many iron atoms are there in a block of alloy measuring$10cm \times 20cm \times 15cm$?
A. $2.201 \times {10^{26}}$
B. $1.442 \times 1{0^{26}}$
C. $8.41 \times {10^{25}}$
D. $6.19 \times {10^{26}}$

Answer 1

Hint: An alloy is a metallic substance which is a combination of metals or metals combined with one or more other elements as either a compound or a solution. Examples are bronze, steel, brass, etc. It is composed of two or more elements like a solution or compound.

Complete step by step answer:
Alloy is a homogeneous solution of a metal with one or more metal or non- metal. A combination of the metallic elements like copper and gold produces red gold, silver and copper produces sterling silver, and gold and silver combination results in white gold. These are examples of an alloy. There are five common alloying elements are Ni, Mn, Cr, V, and Mo. Mostly alloys are made by mixing metals in the molten state and then it is poured into metal and sand moulds after that it is allowed to solidify. Firstly the ingredients are melted then the others are added to it and leave it to dissolve.
According to the question; Given: Density of the block of alloy = $8.17g/c{m^3}$.
Volume of the block of alloy = $\left( {10 \times 20 \times 15} \right)c{m^3}$= $3000c{m^3}$
Using the formula of density = mass/volume
Mass of the block of alloy = density of the alloy $ \times $volume of the block of alloy = $8.17 \times 3000$=$24510g$.
Percentage of iron in alloy =$54.7\% $.
Iron present in the block of alloy = $54.7/100 \times 24510$=$13406.9g$.
Molar mass of iron = $55.847g/mol$
By using molar mass, we convert mass into moles i.e. no. of moles = given mass/molecular mass.
Moles of iron = $13406.9/55.847 = 240.06moles$
Number of atoms of iron = $240.06 \times 6.023 \times 1{0^{23}} = 1.445 \times {10^{26}}atoms$.

So, the correct answer is Option B.

Note:
Students must remember that gram should be converted into moles. All quantities should be in its SI unit. Steel alloy is the strongest known metal in the universe. It is divided into two groups: low alloy steels and high alloy steels.