Question

What volume, in liters, is occupied by 1.5 x 1023 atoms of argon gas (Ar) at STP?

Answer 1

The volume of Argon gas is 5.60L

Explanation:

Given information:

The number of atoms of argon = 1.5 x 10^23 atoms

To find the volume of Argon, we need to find the number of moles of argon, then, we assume the number of moles of argon to be x

To find the number of moles, we will need to apply the below formula

`\text{Number of atoms = mole x Avogadro's number}`

Recall that, Avogadro's number = 6.022 x 10^23

`\begin{gathered} 1.5\cdot10^(23)\text{ = x }\cdot\text{ 6.022 }\cdot10^(23) \\ \text{Isolate x by dividing through by 6.022 }\cdot10^(23) \\ x\text{ = }(1.5\cdot10^(23))/(6.022\cdot10^(23)) \\ x\text{ = 0.2498 mole} \end{gathered}`

Since x represents the number of moles of argon gas, then, the mole of argon gas is 0.2498 mole.

The next step is to find the volume of Argon in liters

Recall that, at S.T.P, 1 mole is equivalent to 22.4L

Let x represent the volume in liters of argon

Then, this can be solved mathematically below

`\begin{gathered} 1\text{ mole }\rightarrow\text{ 22.4 L} \\ 0.2498\text{ mole }\rightarrow\text{ xL} \\ \text{Mathematically,} \\ 1\text{ = 22.4} \\ 0.2498\text{ = x} \\ \text{Cross multiply} \\ 1\cdot\text{ x = 0.2498 }\cdot\text{ 22.4} \\ x\text{ = }5.60L \end{gathered}`

Therefore, the volume of Argon gas is 5.60L