JEE Advance - Chemistry (1980 - No. 3)
Explanation
To find the total number of electrons in 18 ml of water, we need to follow a series of steps involving concepts from chemistry, particularly Avogadro's number and the composition of water molecules.
First, let's determine the number of moles of water in 18 ml. The density of water is approximately 1 g/ml, so 18 ml of water would have a mass of 18 grams.
The molar mass of water (H2O) is 18 g/mol (approximately 1 g/mol for Hydrogen and 16 g/mol for Oxygen, hence 2*1 + 16 = 18 g/mol). To calculate the number of moles of water, we use the formula:
$$\text{moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}}$$
Substituting the given values:
$$\text{moles of water} = \frac{18 \text{ g}}{18 \text{ g/mol}} = 1 \text{ mol}$$
Now, each water molecule contains 10 electrons (2 in each hydrogen atom and 6 in the oxygen atom).
To find the total number of electrons in all the water molecules, we multiply the number of moles of water by Avogadro's number (which is approximately $$6.022 \times 10^{23}$$ molā1) to get the number of molecules, then multiply that by the number of electrons per molecule:
$$\text{Total electrons} = \text{moles of water} \times \text{Avogadro's number} \times \text{electrons per molecule}$$
Substituting the values we know:
$$\text{Total electrons} = 1 \text{ mol} \times 6.022 \times 10^{23} \text{ mol}^{-1} \times 10$$
$$\text{Total electrons} = 6.022 \times 10^{24}$$
Therefore, there are $$6.022 \times 10^{24}$$ electrons in 18 ml of water.
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