Question

How many moles of water are in a 710-gram bottle of water?

Answer 1

A mole is a unit of measurement for amount of a substance that is accepted widely as an SI unit. The number of atoms in one mole of any substance is defined to be, $6.023 \times {10^{23}}$ . This value is called the Avogadro number. The number of moles of a substance is also closely related to its molar mass.

Formulas used: We will be using the formula, $n = \dfrac{{{m_s}}}{{{M_s}}}$
where $n$ is the number of moles of a particle, ${m_s}$ is the mass of the sample taken, and ${M_s}$ is the molar mass of the compound of which the sample is taken.

Complete step-by-step answer: We know that the mole is a unit of measurement for amount of a substance that is accepted as the SI unit for measuring the amount of a substance. 1 mole of any substance is supposed to contain Avogadro number of particles (atoms, molecules, protons or electrons). The Avogadro number is numerically given by, $6.023 \times {10^{23}}$ .
The molar mass of a substance is nothing but the mass of one mole of that substance in grams, but the amount of substance in a sample is given by the number of moles of the substance in the sample. Practically the molar mass of any substance is taken to be the mean molecular mass of that substance. Thus, the number of moles of a substance can be found by dividing the mass of the sample by the molar mass of the compound.
$n = \dfrac{{{m_s}}}{{{M_s}}}$
We know that the molecular mass of a water molecule is ${M_{{H_2}O}} = 18{\text{g}}$ and the mass of the given sample is ${m_{{H_2}O}} = 710{\text{g}}$ . To find the number of moles of water in the given sample,
$n = \dfrac{{710}}{{18}}$
$n = 39.45$
Thus, there are $39.45$ moles in the given water sample of 710 g.

Note: However, the number of water molecules in the given sample of water will be $39.45 \times \left( {6.023 \times {{10}^{23}}} \right)$ molecules.