Acids And Bases

Step 1: Use the Bohr radius formula for hydrogen-like atoms. The radius of the -th orbit for a hydrogen-like atom is given by: where is the principal quantum number, is the atomic number (2 for helium), is the reduced mass (approximately the electron mass for light ions), is the elementary charge, and is the reduced Planck's constant.
Step 2: Plug in the values for the second orbit ( ). For the ion in its second orbit:

Step 1: Understanding Essential Amino Acids.
- Amino acids are organic compounds containing amino (-NH and carboxyl (-COOH) functional groups.
- Essential amino acids cannot be synthesized by the human body and must be obtained from dietary sources.

Step 2: Identifying the Essential Amino Acid.
- Valine ( ) is an essential amino acid.
- It is necessary for muscle growth, tissue repair, and energy production.
- The other given options include:
- Alanine ( ) – a non-essential amino acid.
- Serine ( ) – a non-essential amino acid.
- Cysteine ( ) – a non-essential amino acid.

Step 3: Conclusion. Since valine is an essential amino acid that must be obtained through diet, option (3) is correct.

Understanding each metal's refining process:
A. Zn - Distillation: Zinc is refined by distillation due to its low boiling point, separating it from impurities with higher boiling points.
B. Sn - Liquation: Tin is refined using liquation, where impurities with different melting points are separated by heating the metal.
C. Ga - Zone refining: Gallium is refined by zone refining, where a molten zone moves along the metal, effectively purifying it by removing impurities.
D. Zr - Vapour phase refining: Zirconium is refined using vapour phase refining, where it reacts with chlorine to form ZrCl4, which is then distilled. Thus, all the given pairs are correct.

Step 1: Analyze the molecular geometries.
Set i: Both molecules are tetrahedral, sharing identical electron pair geometries.
Set ii: Both molecules have a pyramidal structure, albeit with bonding pairs and with lone pairs affecting the structure.
Set iii: Both are linear, having the simplest geometric arrangement.
Step 2: Comparison with Set iv. Set iv does not contain isostructural molecules due to the different spatial arrangements ( see-saw vs. square planar).

The ionization constant of the conjugate acid can be found using the relation: Where: - is the ionization constant of the conjugate acid, - is the ionization constant of , - is the ionization constant of water. Given that , we can solve for : Thus, the ionization constant of the conjugate acid is .
Final Answer: .

Step 1: Understanding Tollen’s Test Ammoniacal silver nitrate ( ) is used in Tollen’s test to detect reducing sugars. A reducing sugar has a free aldehyde or ketone group that can reduce to metallic silver.

Step 2: Identifying Reducing and Non-Reducing Sugars - Sucrose is a non-reducing sugar because its glycosidic bond prevents the free aldehyde or ketone group from participating in the reaction. - Maltose, lactose, and fructose are reducing sugars, which means they react with ammoniacal .

Step 3: Conclusion Since sucrose does not react with Tollen’s reagent, it is the correct answer.

Step 1: Set up the initial and equilibrium concentrations. Given that one mole each of AB and CD reacts, at equilibrium: - moles (remaining) - moles (formed)
Step 2: Write the expression for the equilibrium constant (K).
Step 3: Plug in the equilibrium concentrations.