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One molecule of water(H2O)contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of1.0uand an atom of oxygen has a mass of 16u, approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world鈥檚 oceans, which have an estimated total mass of 1.41021kg?

Short Answer

Expert verified

( a ) The mass of one molecule of water is 30.0010-27kg.

( b ) Number of molecules of water present in the world鈥檚 oceans is 51046kg.

Step by step solution

01

Given data

The mass of the hydrogen atom is1.0u .

The mass of the oxygen atom is16u .

The mass of water in the ocean is1.41021kg .

02

Understanding the unit conversion

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors.

03

(a) Determination of the mass in kg.

The atomic mass unit of H2O is,

16u+1u+1u=18u

Here, 16uis the atomic mass unit of oxygen and 1uis the atomic mass unit of hydrogen.

It is known that,1u=1.6605388610-27

Now, convert it into kilograms.

Mass of water molecule m in kg is calculated as,

m=(18u1.6605388610-27kg1u)=29.88910-27kg30.0010-27kg

Thus, the mass of the water molecule is30.0010-27.

04

(b) Determination of the number of molecules.

For the calculation of the number of molecules of water present in the world鈥檚 oceans with some estimated mass, divide the total mass by the mass of each molecule and obtain the (approximate) number of water molecules. Therefore,

Numberofmolecules=TotelmassofoceanMassofonewatermolecule=1.410-21kg30.010-27kg=0.046610484.67104651046

Thus, the number of molecules is51046 .

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