Henry's law constant for CO 2 ​ in water is 1.67×10 ∘ Pa at 298 K . Calculate the quantity of CO 2 ​ in 500 mL , of soda water when packed under 2.5 atm CO 2 ​ pressure at 298 K .

 

Explanation

To calculate the amount of CO${}_2$ dissolved, we use Henry's Law:

$$P=k_H\times x\_C{O}_2$$

where:\

• $P$ = partial pressure of CO${}_2$ above solution \
• $k_H$ = Henry's Law constant (in Pa)
• $x_{C{O}_2}$ = mole fraction of CO${}_2$ in solution

We will:

1. Convert the pressure to Pascal (SI unit).
2. Use Henry's Law to find $x_{C{O}_2}$.
3. Use the definition of mole fraction to calculate moles of CO${}_2$ present in 500 ml of water.

Step-By-Step Solution

Step 1

Convert the pressure from atm to Pa:

$1\text{atm}=1.013\times 10^5\text{Pa}$

So, $$2.5\text{atm}=2.5\times 1.013\times 10^5=2.5325\times 10^5\text{Pa}$$

Step 2

Apply Henry's Law to find $x_{C{O}_2}$:

$$x_{C{O}_2}=\frac{P}{k_H}=\frac{2.5325\times 10^5}{1.67\times 10^8}$$ $$x_{C{O}_2}=1.517\times 10^{-3}$$

Step 3

Let the number of moles of water in 500 mL: (Since soda water is so dilute that it is as good as water, hence we take water as the SOLVENT and hence MOLAR MASS of WATER i.e. 18g is taken for calculation, intead of that of SODA  WATER (soda water is Carbonic Acid H2CO3   Molar mass 62g) dissolved in WATER)

• Density of water $\approx 1\text{g/mL}$
• Mass of water $=500\text{mL}\times 1\text{g/mL}=500\text{g}$
• Molar mass of H${}_2$O $=18\text{g/mol}$
• Moles of H${}_2$O $=\frac{500}{18}=27.78\text{mol}$

Let $n$ = moles of CO${}_2$ dissolved in 500 mL of water.

By mole fraction definition: $$x_{C{O}_2}=\frac{n}{n+27.78}$$

Since $n$ is much less than 27.78, $n+27.78\approx 27.78$ (approximation valid for dilute solutions): $$x_{C{O}_2}\approx \frac{n}{27.78}$$ $$1.517\times 10^{-3}=\frac{n}{27.78}$$ $$n=1.517\times 10^{-3}\times 27.78=0.04214\text{mol}$$

Step 4

Convert moles of CO${}_2$ to mass if required:

Molar mass of CO${}_2$ = $44\text{g/mol}$ $${\text{Mass of CO}}_2=0.04214\times 44=1.85\text{g}$$

Final Answer

The quantity of CO${}_2$ dissolved in 500 mL of soda water at 2.5 atm is:

$$0.0421\text{mol}\text{or}1.85\text{g (rounded to 3 significant figures)}$$

What are the impurities in 22 carat gold?

 22-carat gold contains 91.67% pure gold and 8.33% other metals (often called alloys) added intentionally to provide strength and durability. 

These added metals—which are not considered impurities but deliberate mixtures—typically include: 

• Copper
• Silver
• Zinc
• Nickel (occasionally) 

Because pure gold (24-carat) is too soft and malleable to hold its shape or bear the weight of daily wear, these non-gold metals are essential for making it suitable for jewelry crafting

Electrons in metals behave like a gas or a liquid

 Electrons in metals behave more like a liquid than an independent gas. While early theories treated them as a simple bouncing "gas," strong electrical repulsions mean they actually flow as a correlated fluid called a Fermi liquid. [1, 2, 3, 4]

The Electron Gas Model

The classical Drude-Sommerfeld model treats conduction electrons as a "free electron gas". [1, 2]

• How it works: Electrons move randomly in all directions, much like molecules in an ideal gas, but they do not bounce off one another.
• What it explains: It successfully predicts basic electrical and thermal conductivity, as well as the heat capacity of metals.
• Why it falls short: It ignores the fact that electrons are highly charged and repel each other. [1, 2, 3, 4, 5]

The Electron Liquid Model (Fermi Liquid Theory)

Because the concentration of electrons in a metal is incredibly high (roughly \(10^{29} \text{ per m}^3\)), they are constantly interacting via Coulomb forces. This requires a quantum fluid approach. [1, 2, 3, 4, 5]

• How it works: Electrons drag and coordinate with one another. Instead of moving independently, they flow collectively as a highly viscous, charged liquid. [1, 2, 3]
• What it explains: It accurately describes complex phenomena like superconductivity, specific types of resistance, and how electrons "screen" or hide the charge of impurities