States of Matter
Question 1: What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30° C?
Answer: Given, p1 = 1 bar, V1 = 500 dm3, V2 = 200 dm3
As per Boyle’s Law: p1V1 = p2V2
Or, `p_2=(500)/(200)=2.5` bar
Question 2: A vessel of 120 mL capacity contains a certain amount of gas at 35° C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35°C. What would be its pressure?
Answer: Given, p1 = 1.2 bar, V1 = 120 mL, V2 = 180 mL
As per Boyle’s Law: p1V1 = p2V2
Or, `p_2=(1.2xx120)/(180)=0.8` bar
Question 3: Using the equation of state pV = nRT; show that at a given temperature density of a gas is proportional to gas pressure p.
We know that n = constant mass of gas ÷ molar mass of gas `=m/M`
So, `p∝ρ` proved
Question 4: At 0° C, the density of a certain dioxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?
Answer: Molar mass of dinitrogen = 28 u
From previous question, we found
As R is a constant and given temperature is same
Or, `M_1=(5xx28)/2=70` u
Question 5: Pressure of 1 g of an ideal gas A at 27° C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find the relationship between their molecular masses.
Answer: Let us assume that molar masses of A and B are MA and MB respectively. So, their number of moles can be as follows:
Given, pA = 2 bar, pA + pB = 3 bar
So, pB = 3 – 2 = 1 bar
Using the equation, pV = nRT, we get
Question 6: The drain cleaner, Drainex contains small bits of aluminum which react with caustic soda to produce dihydrogen. What volume of dihydrogen at 20° C and one bar will be released when 0.15 g of aluminum reacts?
Answer: The chemical reaction of this process is given by following equation:
2Al + 2NaOH + H2 → 1NaAlO2 + 3H2
In this reaction, 2 M of aluminium produces 3 M of dihydrogen gas.
Molar mass of Al = 2 × 27 = 54 g
Volume of hydrogen produced at STP = 3 × 22720 mL
So, volume of hydrogen produce on reaction with 0.15 g
Now, we have: V1 = 189.33 mL, p1 1 bar, p2 = 1 bar, T1 = 273 K and T2 = 20 + 273 = 293 K
Volume V2 can be calculated as follows:
According to ideal gas equation:
Question 7: What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of carbon dioxide contianed in a 9 dm3 flask at 27° C?
Answer: Molar mass of methane = 16 u and molar mass of CO2 = 24 u
So, n of methane = `(3.2)/(16)=0.2`
And, n of carbon dioxide = `(4.4)/(44)=0.1`
R = 8.314 J K-1 mol-1
Given temperature = 27 + 273 = 300 K
Using pV = nRT
So, pmethane `=(0.2xx0.08314xx300)/9=0.55` atm
And, pcarbon dioxide `=(0.1xx0.08314xx300)/9=0.27` atm
So, pressure exerted by both gases together = 0.55 + 0.27 = 0.82 atm
Question 8: What will the pressure of the gaseous mixture when 0.5 L of H2 at 0.8 bar and 2.0 L of of dioxygen at 0.7 bar are introduced in a 1L vessel at 27° C?
Answer: Calculation of partial pressure of H2: p1 = 0.8 bar, p2 = ?, V1 = 0.5 L and V2 = 1 L
Or, `p_2=0.8xx0.5=0.4` bar
Calculation of partial pressure of O2: p1 = 0.7 bar, p2 = ?, V1 = 2 L and V2 = 1 L
Or, `p_2=1.4` bar
Total pressure = 0.4 + 1.4 = 1.8 bar
Question 9: Density of a gas is found to be 5.46 g/dm3 at 27° C at 2 bar pressure. What will be its density at STP?
Answer: We know: `d=p/(RT)`
Given, d1 = 5.46, p1 = 2 bar,T1 = 300 K, p2 = 1 bar,T2 = 273 K
We have, `(5.46)/(d_2)=(2xx273)/(1xx300)`
Or, `d_2=(5.46xx300)/(2xx273)=3` g/dm3
Question 10: 34.05 mL of phosphorus vapor weighs 0.0625 g at 546° C and 0.1 bar pressure. What is the molar mass of phosphorus?
Answer: Given: V1 = 34.05 mL, T1 = 546 + 273 = 819 K, p1 = 0.1 bar, m = 0.0625 g
Let us calculate the volume at STP (T2 = 273 K, p2 = 1 bar
Since 11.35 mL weighs 0.0625 g at STP
So, 22720 mL weighs `(0.0625)/(11.35)xx22720=125` g
So, molar mass = 125 g mol-1