BuyFind

Precalculus: Mathematics for Calcu...

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

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

Answer to Problem 99E

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!