Question

The protonic charge in \(100 \mathrm{gm}\) of water is \(\ldots \ldots . . \mathrm{c}\) (A) \(4.8 \times 10^{5}\) (B) \(5.4 \times 10^{6}\) (C) \(3.6 \times 10^{4}\) (D) \(4.9 \times 10^{6}\)

Short answer

The protonic charge in 100 gm of water is approximately \( 5.4 \times 10^{6} \) C.

Step-by-step solution

Calculate the number of moles of water

First, we need to determine the number of moles of water in the given 100 g sample. To find the moles, we will use the formula: Moles = Mass / Molar mass The molar mass of water (H₂O) is the sum of the atomic masses of two hydrogen atoms (each 1 g/mol) and one oxygen atom (16 g/mol): Molar mass of water = 2 * 1 + 16 = 18 g/mol. Now we can calculate the moles of water in the sample: Moles of water = \( \frac{100 \text{ g}}{18 \text{ g/mol}} \) = 5.56 moles (rounded to two decimal places).

Calculate the number of protons in the moles of water

Next, we will find the number of protons in the 5.56 moles of water. Water has 10 protons per molecule: 8 protons from the oxygen atom and 1 proton from each of the two hydrogen atoms. To find the total number of water molecules in the sample, we will use the formula: Number of molecules = Moles × Avogadro's number Avogadro's number is \( 6.022 \times 10^{23} \) molecules/mol. Number of water molecules = 5.56 moles × \( 6.022 \times 10^{23} \) molecules/mol = \( 3.348 \times 10^{24} \) molecules Now, we can find the total number of protons in the sample by multiplying the number of water molecules by the number of protons per water molecule: Total number of protons = \( (3.348 \times 10^{24} \) water molecules) x (10 protons/water molecule) = \(3.348 \times 10^{25} \) protons

Calculate the protonic charge

Finally, we will calculate the protonic charge using the total number of protons in the sample. The charge of a single proton is approximately \( 1.6 \times 10^{-19} \) C (Coulombs). To find the total protonic charge, we will multiply the charge of a single proton by the total number of protons: Protonic charge = \( (1.6 \times 10^{-19} \text{ C/proton}) \times (3.348 \times 10^{25} \text{ protons}) = 5.3568 \times 10^{6} \text{ C} \) Comparing with the given options, we can round the protonic charge to \( 5.4 \times 10^{6} \) C. Therefore, the correct answer is (B) \( 5.4 \times 10^{6} \) C.

Key concepts

Moles Calculation

To find out how many moles are in a particular sample, we use the moles calculation. Moles represent a basic quantity unit in chemistry used to measure the number of particles, like atoms or molecules, in a substance. The formula to calculate moles is \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} \].
For instance, in the problem provided, we needed to determine the number of moles of water in a 100 g sample. By using the molar mass of water, which is calculated as 18 g/mol, determined by adding up the atomic masses of its constituents (2 hydrogens and 1 oxygen), we used this formula:
\[ \text{Moles of water} = \frac{100 \text{ g}}{18 \text{ g/mol}} = 5.56 \text{ moles} \].
This calculation helps us understand the specific quantity of substance we are working with, making it easier to calculate reactions and related properties.

Avogadro's Number

Named after scientist Amedeo Avogadro, Avogadro's number is a fundamental constant in chemistry. This number is used to connect macroscopic and microscopic worlds by allowing us to count atoms and molecules in a given amount of substance.
Avogadro's number is given as \( 6.022 \times 10^{23} \text{ particles/mol} \), meaning one mole of any substance contains that many molecules or atoms.
In the context of our exercise, once we calculated the moles of water, we used Avogadro's number to find out the total number of molecules. The formula applied was:
\[ \text{Number of molecules} = \text{Moles} \times \text{Avogadro’s number} \].
For 5.56 moles of water, the calculation of molecules was:\[ 5.56 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 3.348 \times 10^{24} \text{ molecules}\].
By understanding Avogadro's number, we can relate the number of particles in the lab to its measurable volume or mass, allowing more in-depth explorations of chemistry.

Molar Mass

Molar mass plays a crucial role in stoichiometry. It refers to the mass of one mole of a substance (gram/mole) and is derived from the atomic masses of the constituents. It helps in converting a substance's mass from grams to moles, facilitating chemical calculations.
To determine molar mass, you must first identify the elements present in the molecule and their atomic masses, found on the periodic table, and then sum these values:
- For water (\( \text{H}_2\text{O} \)): - Hydrogen has an atomic mass of 1 g/mol. Since there are 2 hydrogen atoms, their combined mass is 2 g/mol. - Oxygen has an atomic mass of 16 g/mol.Thus, the molar mass of water is:
\[ \text{Molar mass of water} = 2 + 16 = 18 \text{ g/mol} \].
Understanding and calculating molar mass is essential when translating between quantities of substances in grams and in moles, a foundational aspect of solving many chemistry problems.

Coulomb Charge

In physics and chemistry, understanding charge is essential, particularly when calculating the protonic charge. Charge quantifies the amount of electricity in a substance, measured in coulombs, which is the SI unit for electric charge.
Each proton carries a positive charge of approximately \( 1.6 \times 10^{-19} \text{ C} \) (Coulombs). To find the total charge in a sample, multiply the number of protons by the charge of a single proton.
In the exercise, after calculating the number of protons (\( 3.348 \times 10^{25} \)), we determined the total charge by:\[ \text{Protonic charge} = (1.6 \times 10^{-19} \text{ C/proton}) \times (3.348 \times 10^{25} \text{ protons}) = 5.3568 \times 10^{6} \text{ C}\].
This understanding of charge makes it possible to calculate and predict behaviors in electrochemistry and various fields where electricity plays a part.