Avogadros Law and Ideal Gas Equation - UNSOLVED PRACTICE SET

Q7. State Avogadro's Law. What is the significance of Avogadro's constant (6.022 × 10²³)?

Q8. Derive the ideal gas equation by combining Boyle's Law, Charles's Law, and Avogadro's Law.

Q9. What is meant by STP? Calculate the volume occupied by 5.0 g of CO₂ at STP. (Molar mass of CO₂ = 44 g/mol)

Q10. Write the ideal gas equation in terms of density. How can you use this to calculate the molar mass of an unknown gas?

Q11. A balloon contains 2.0 moles of helium at 300 K and 1.0 atm. Calculate the volume of the balloon. (R = 0.0821 L·atm/mol·K)

Q12. Explain why the ideal gas equation is called 'ideal.' Under what conditions do real gases deviate from ideal behaviour?

Q13. (a) State Avogadro's Law and explain its significance. How does it help in determining molecular formulas?

(b) Calculate the number of molecules in 11.2 L of O₂ gas at STP.

(c) Two gases A and B have densities 1.5 g/L and 3.0 g/L respectively at the same temperature and pressure. What is the ratio of their molar masses?

Q14. (a) Derive the ideal gas equation: PV = nRT. Explain the significance of each term.

(b) Calculate the pressure exerted by 5.0 moles of CO₂ in a 10.0 L container at 300 K. (R = 0.0821 L·atm/mol·K)

(c) A student claims that the value of the gas constant R depends on the nature of the gas. Is the student correct? Explain.

Q15. (a) Derive the following forms of the ideal gas equation:

(i) d = PM/RT (where d is density)

(ii) PM = dRT

(iii) PV = (w/M)RT (where w is mass and M is molar mass)

(b) The density of a gas at STP is 1.25 g/L. Calculate its molar mass.

(c) A compound contains C, H, and O only. When vaporised, 0.50 g of the compound occupies 200 mL at STP. Calculate the molecular mass of the compound.

Q16. Solve the following problems using the ideal gas equation:

(a) Calculate the volume occupied by 8.0 g of O₂ at 300 K and 2.0 atm pressure. (R = 0.0821 L·atm/mol·K, M of O₂ = 32 g/mol)

(b) Calculate the number of moles of CO₂ present in a 5.0 L cylinder at 300 K and 5.0 atm pressure.

(c) A gas has a density of 2.5 g/L at 300 K and 1.5 atm. Calculate its molar mass.

(d) At what temperature will 2.0 moles of an ideal gas occupy 10.0 L at 5.0 atm pressure?

Q17. A student performs an experiment to determine the molar mass of an unknown gas:

(a) 0.82 g of the gas occupies 400 mL at 300 K and 1.5 atm. Calculate the molar mass of the gas.

(b) The gas is found to contain 80% carbon and 20% hydrogen by mass. Determine its empirical formula.

(c) Using the molar mass from part (a) and the empirical formula from part (b), determine the molecular formula of the gas.

(d) The student repeats the experiment at a higher pressure of 10 atm and finds the calculated molar mass to be slightly different. Explain why this happens for real gases.

Q18. In India, the ideal gas equation has many practical applications:

(a) A CNG (compressed natural gas, mainly methane) cylinder has a volume of 60 L and contains gas at a pressure of 200 atm at 27°C. Calculate the mass of methane in the cylinder. (M of CH₄ = 16 g/mol)

(b) An oxygen cylinder used in hospitals contains 5.0 kg of O₂ at a pressure of 150 atm at 27°C. Calculate the volume of the cylinder.

(c) A weather balloon is filled with helium at 1.0 atm and 27°C, occupying a volume of 1000 L. As it rises, the temperature drops to –23°C and the pressure drops to 0.5 atm. Calculate the new volume of the balloon.

(d) In a school laboratory, a student prepares H₂ gas by reacting zinc with dilute HCl. If 0.65 g of zinc is used, calculate the volume of H₂ gas produced at 300 K and 1.0 atm. (M of Zn = 65 g/mol)