# The number of molecules of oxygen in the room. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.2, Problem 99E
To determine

## The number of molecules of oxygen in the room.

Expert Solution

The number of molecules of oxygen in the room is 4.03×1027molecules_.

### Explanation of Solution

Formula used:

Volumeofasealedroom=Length×Width×Depth

Numberofmoleculesinasealedroom=(Volumeofasealedroom(L))×(Numberofmoleculesin1L)

Calculation:

Given that, the length of a sealed room in a hospital is 10m, the width of a sealed room in a hospital is 5m and the depth of a sealed room in a hospital is 3m.

It is known that, one cubic meter contains 1000 L and 22.4 L of any gas contains 6.02×1023molecules.

Substitute 10m for Length, 5m for Width and 3m for Depth 3.7×103m in the formula to calculate volume of a sealed room.

Volumeofasealedroom=10m×5m×3m=150m3

Use the unit conversion of m3 into L to convert volume of a sealed room in m3 into L.

Volumeofasealedroom=150m3=150×1m3=150×1000L=150000L

Calculate the number of molecules in 22.4 L as follows.

22.4L=6.02×1023molecules1L=6.02×1023molecules22.4L1L=0.26875×1023molecules

Therefore, the number of molecules in 1 L is 0.26875×1023molecules.

Substitute 150000L for volume of a sealed room and 0.26875×1023molecules for number of molecules in 1 L.

Number of molecules in a sealed room=(150000L)×(0.26875×1023molecules)=40312.5×1023molecules

Now, move decimal 4 places to the left and add 4 to the power of 10 to write the above quantity in proper scientific notation as follows.

Numberofmoleculesinasealedroom=40312.5×1023molecules=4.03125×1027molecules

Round off the above quantity to two decimal places.

Numberofmoleculesinasealedroom=4.03125×1027molecules=4.03×1027molecules

Therefore, the number of molecules of oxygen in the room is 4.03×1027molecules_.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!