Question

How many atoms are in 57.5 liters of xenon gas at STP

Answer 1

1.55 × 10²⁴ atoms Xe

General Formulas and Concepts:

Atomic Structure

• Reading a Periodic Table
• Moles
• STP (Standard Conditions for Temperature and Pressure) = 22.4 L per mole at 1 atm, 273 K
• Avogadro's Number - 6.022 × 10²³ atoms, molecules, formula units, etc.

Stoichiometry

• Using Dimensional Analysis

Step-by-step explanation:

Step 1: Define

[Given] 57.5 L Xe at STP

[Solve] atoms Xe

Step 2: Identify Conversions

[STP] 22.4 L = 1 mol

Avogadro's Number

Step 3: Convert

1. [DA] Set up:
   `\displaystyle 57.5 \ L \ Xe((1 \ mol \ Xe)/(22.4 \ L \ Xe))((6.022 \cdot 10^(23) \ atoms \ Xe)/(1 \ mol \ Xe))`
2. [DA] Divide/Multiply [Cancel out units]:
   `\displaystyle 1.54583 \cdot 10^(24) \ atoms \ Xe`

Step 4: Check

Follow sig fig rules and round. We are given 3 sig figs.

1.54583 × 10²⁴ atoms Xe ≈ 1.55 × 10²⁴ atoms Xe