help with section 4, question e. 4. Lake Tahoe has an approximate volume of 36 c

Question

help with section 4, question e.

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 (m-1.00783g/mol) 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

Ans > Volume of the lake is 36 cubic miles = 36 x 4.168 cubic kilometers = 150.048 x 109 m3 [ 1 mile3 = 4.168km3] = 1.5 x 1011 m3 Density of the water present is 1g/ml = 1000 kg/m3 Total mass of water present in the lake is 1.5 x 1014 kg Now suppose that a% of the hydrogen atom are deuterium then the molar mass of D2O would be (2 x 2.01410)+16 = 20.0282g/mole. Now the remaining (100-a)% would be hydrogen atoms and the molar mass of H2O would be (2 x 1.00783) + 16 = 18.01566g/mole.

But the average molar mass of hydrogen present is 1.00794 g/mole. Then the avergae molar mass of water molecules present would be (2 x 1.00794)+16 = 18.01588g/mole = 18.01558 x 10-03kg/mole Total number of molecules present is 1.5 x 1014kg/(18.01558 x 10-03) = 8.326 x 1015moles

Now, if a% of molecules are D2O then there is (a/100) fractions of D2O and simmlilarly there is (100-a)/100) fractions of H2O. Therefore, (a/100)MD20 + {(100-a)/100}MH20 = average mass of the water present => (a/100)20.0282 + {(100-a)/100}18.01556 = 18.01558 => 20.0282a + 1801.556 - 18.01556a = 1801.558 => 2.01264a = 0.002 => a = 0.0009918% Deuterium is present Total number of moles of deuterium present is (0.0009918/100) x (8.326 x 1015) = 8.25 x 1010moles of deuterium is present in the Lake Tahoe

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.