please help with section 4, question a. 4. Lake Tahoe has an approximate volume

Question

please help with section 4, question a.

4. Lake Tahoe has an approximate volume of 36 cubic miles. Assuming density of water is 1.00g/cm and that every molecule of water has two hydrogen atoms and one oxygen atom: a. What is the mass of the water in Lake Tahoe in kilograms and in gigagrams? b. How many moles of water molecules are there in Lake Tahoe? c. What is the volume of a single water molecule in mL? What about in cubic nanometers? d. Hydrogen has two stable isotopes: hydrogen-1 (ms] 00783g/md) and hydrogen-2 (also called deuterium, m-2.01410g/mol). If the atomic mass of hydrogen is 1.00794g/mol, what percentage of hydrogen atoms are deuterium? How many moles of deuterium atoms are in Lake Tahoe? e.

Explanation / Answer

a)

Given:

Volume of Lake Tahoe = 36 Cubic Miles

Density of water =1g/cm3

Mass of water in of Lake Tahoe = Volume of Lake Tahoe x Density of water

Density of water is in 1g/cm3, so convert the volume of water in cm3

Step1: Convert Cubic Miles into Cubic Km

1 Cubic Miles = 4.1682 Cubic Kilometers

36 Cubic Miles = 4.1682 x 36 = 150.05 Cubic Kilometers

Step2: Convert Cubic Km into Cubic cm

1 km3 = 1.0 x 10^15 cm3

150.05 km3 = 150.05 x 1.0 x 10^15 cm3 = 1.501 x 10^17 cm3

Step 3: Calculate mass of water in of Lake Tahoe

Mass of water in of Lake Tahoe = Volume of Lake Tahoe x Density of water

                                                          = 1.501 x 10^17 cm3 x 1 g/ cm3

                                                          = 1.501 x 10^17 grams

Step4: Convert grams into kilograms

1000 grams = kilograms

1.501 x 10^17 grams =1.501 x 10^17 /10^3 = 1.501 x 10^14 kilograms

Mass of water in of Lake Tahoe = 1.50 x 10^14 kilograms

Step5: Convert kilograms into

10^6 kg = 1 gigagram

So, 1.50 x 10^14 kilograms = 1.50 x 10^14 / 10^6 = 1.50 x 10^8 gigagrams

Mass of water in of Lake Tahoe = 1.50 x 10^8 gigagrams

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