Question

How many grams does an atom of hydrogen weigh?

Answer 1

Hint: The mass of 1 mole of a compound is known as molar mass, the mole concept gives us an estimate about the number of atoms present in1 molar mass of a compound. Using the mole concept formula, we can then find the number of atoms in the molar mass of the compound. From there, we can calculate the weight of 1 atom of the substance given.
Formula used:
\[{\rm{Moles = }}\dfrac{{{\rm{weight}}}}{{{\rm{molar mass}}}}\] where molar mass is the mass of 1 mole of a compound.

Complete step by step answer:
The mole concept states that 1 mole of an atom or molecule consists of the same amount of particles in it. The number of particles in 1 mole is known as Avogadro’s number. It is equal to \[6.023 \times {10^{23}}\] atoms or molecules. The mass of 1 mole is different for every compound. We know that the molar mass of hydrogen is \[{\rm{1 g mo}}{{\rm{l}}^{{\rm{ - 1}}}}\]. So, according to the mole concept, 1 mole of hydrogen consists of \[6.023 \times {10^{23}}\] atoms. We can also write this as:
\[{\rm{1 mole hydrogen = 6}}{\rm{.023 \times 1}}{{\rm{0}}^{{\rm{23}}}}{\rm{ particles}}\]
From the mole concept formula: \[{\rm{1 mole of hydrogen = }}\dfrac{{{\rm{1 g}}}}{{{\rm{1 g mo}}{{\rm{l}}^{{\rm{ - 1}}}}}}\].
So, the weight of 1 mole of hydrogen is 1g.
\[ \Rightarrow {\rm{1g hydrogen = 6}}{\rm{.023 \times 1}}{{\rm{0}}^{{\rm{23}}}}{\rm{ particles}}\]
\[ \Rightarrow {\rm{6}}{\rm{.023 \times 1}}{{\rm{0}}^{{\rm{23}}}}{\rm{ particles = 1g hydrogen}}\]
From here, we can now calculate the mass of 1 atom of hydrogen:
\[ \Rightarrow {\rm{1 atom hydrogen = }}\dfrac{1}{{6.023 \times {{10}^{23}}}}g\]
Solving this equation, we get:
\[{\rm{1 atom hydrogen = 0}}{\rm{.166}} \times {10^{ - 23}}g\]

\[\therefore\] The weight of 1 atom of hydrogen will be \[1.66 \times {10^{ - 24}}g\].

Note:
The molar mass of a molecule will be different from the molar mass of an atom of the same element. For example, hydrogen as an atom has molar mass of \[{\rm{1 g mo}}{{\rm{l}}^{ - 1}}\] while hydrogen molecule has a molar mass of \[{\rm{2 g mo}}{{\rm{l}}^{ - 1}}\]. This is because the hydrogen molecule is present as \[{{\rm{H}}_{\rm{2}}}\]. So, the mass is double the mass of an atom of hydrogen. While solving the question, we should be aware if the question contains an atom of the element or a molecule.