b) 3.0 x 1023
c) 6.0 x 1023
d) 1.2 x 1024
C is correct. 6.0 x 1023.
For every mole of H2O, there are two moles of hydrogen atoms. We can find the number of moles of H2O using the given mass in the question stem and the molar mass. The molar mass of H2O is 2 g/mol (2 H) + 16 g/mol (O) = 18 g/mol. Therefore, the number of moles of H2O is 9 g / 18 g/mol = 0.50 mol. Using our previous reasoning, if there are 0.50 moles of H2O, there is 1 mole of hydrogen atoms. Thus, the number of hydrogen atoms is simply equal to Avogadro’s number: 6.0 x 1023.
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As we will discuss in future lessons, the relationship between different reactants and products in a reaction has less to do with their mass or weight and is instead a function of their quantity. However, while the mass of a solution or substance can be easily measured in a laboratory setting, determining the quantity of molecules in a substance is less immediately clear. This brings us to our next major concepts: molecular weight, molar mass, the mole, and Avogadro’s number.
The molecular weight of a molecule is simply the summation of the individual weights of each atom in a molecule. These can be determined by looking at the periodic table. In the example of sodium hydroxide, we would add the atomic weight of sodium (23 Daltons, or Da), oxygen (16 Da), and hydrogen (1 Da), giving us a molecular weight of approximately 40 Da for sodium hydroxide.
The number of molecules in a sample can be determined by dividing the mass of the sample by 40 Da. However, due to the extremely high number of molecules in even a minuscule sample of a chemical substance, this conversion quickly becomes impractical. Therefore, we will instead typically use the more accessible value of molar mass, which is defined as the mass of a compound (in grams) present in one mole (the SI unit of quantity) of that substance. The molar mass of a molecule typically has the same absolute value as its molecular weight. So the molar mass of sodium hydroxide, which had a molecular weight of 40 Da, would be approximately 40 grams per mole.
A mole, which we mentioned above, is a value of quantity equal to 6.02 x 1023 particles of whatever is being measured. This number is referred to as Avogadro’s number, and was determined experimentally by a 19th century Italian scientist named Amedo Avogadro, by dividing the mass of 12 grams of carbon-12 by the mass of a single atom of carbon-12. This conversion allows us to work with the extremely high values of molecular quantity more intuitively: instead of viewing 12 grams of carbon-12 as consisting of an almost unfathomably large number of atoms, we can simply describe it as consisting of one mole of carbon atoms.
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