   Chapter 2.8, Problem 3.4ACP

Chapter
Section
Textbook Problem

Given that the density of argon is 1.78 g/L under standard conditions of temperature and pressure, how many argon atoms are present in a room with dimensions 4.0 m × 5.0 m × 2.4 m that is filled with pure argon under these conditions of temperature and pressure?

Interpretation Introduction

Interpretation: The numbers of argon atoms present in room with given dimensions has to be calculated.

Concept introduction:

Moles: One mole is equivalent to the mass of the substance consists same number of units equal to the atoms present in 12g of 12C.

From given mass of substance moles could be calculated by using the following formula,

Molesofsubstance GivenmassofsubstanceMolecularmass

Equation for number of atoms is,

Number of moles×6.022×1023atoms=number of atoms

Equation for density from volume and mass is,

Density=MassVolume

Explanation

The dimensions of the room are given that 4m×5m×2.4m.

Therefore, the volume of the room is,

4m×5m×2.4m=48m3=48m3×1L103=4.8×104L

The density of the argon is given as 1.78g/L.

Equation for mass from volume and density is,

Density×Volume=Mass

Therefore, the mass of argon cube is,

1.78g/L×4.8×104L=8.54×104g

Conversion formula for mass of an atom and number moles,

Numberofmoles=MassingramsMo

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