Advertisements
Advertisements
प्रश्न
The density of an ideal gas is 1.25 × 10−3 g cm−3 at STP. Calculate the molecular weight of the gas.
Use R=8.31J K-1 mol-1
Advertisements
उत्तर
Let:
m = Mass of the gas
M = Molecular mass of the gas
Now,
Density of ideal gas,\[\rho\]= 1.25 × 10−3 gcm−3 =1.25 kgm−3
Pressure, P = 1.01325\[\times\]105 Pa (At STP)
Temperature, T = 273 K (At STP)
Using the ideal gas equation, we get
\[PV = nRT . . . (1)\]
\[n = \frac{m}{M} . . . (2)\]
\[ \therefore PV = \frac{m}{M}RT\]
\[ \Rightarrow M = \frac{m}{V}\frac{RT}{P}\]
\[ \Rightarrow M = \rho\frac{RT}{P}\]
\[ \Rightarrow M = 1 . 25 \times \frac{8 . 31 \times 273}{{10}^5}\]
\[ \Rightarrow M = 2 . 83 \times {10}^{- 2} \]
\[ = 28 . 3 g - {\text { mol }}^{- 1} \]
APPEARS IN
संबंधित प्रश्न
Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3Å.
An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C?
Calculate the mass of 1 cm3 of oxygen kept at STP.
Find the ratio of the mean speed of hydrogen molecules to the mean speed of nitrogen molecules in a sample containing a mixture of the two gases.
Use R = 8.314 JK-1 mol-1
Figure shows a vessel partitioned by a fixed diathermic separator. Different ideal gases are filled in the two parts. The rms speed of the molecules in the left part equals the mean speed of the molecules in the right part. Calculate the ratio of the mass of a molecule in the left part to the mass of a molecule in the right part.
Estimate the number of collisions per second suffered by a molecule in a sample of hydrogen at STP. The mean free path (average distance covered by a molecule between successive collisions) = 1.38 × 10−5 cm.
Use R = 8.31 JK−1 mol−1
Hydrogen gas is contained in a closed vessel at 1 atm (100 kPa) and 300 K. (a) Calculate the mean speed of the molecules. (b) Suppose the molecules strike the wall with this speed making an average angle of 45° with it. How many molecules strike each square metre of the wall per second?
Use R = 8.31 JK-1 mol-1
A vertical cylinder of height 100 cm contains air at a constant temperature. The top is closed by a frictionless light piston. The atmospheric pressure is equal to 75 cm of mercury. Mercury is slowly poured over the piston. Find the maximum height of the mercury column that can be put on the piston.
Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CAand CB be the molar heat capacities for the two processes,
The value of Cp − Cv is 1.00 R for a gas sample in state A and 1.08 R in state B. Let pAand pB denote the pressures and TA and TB denote the temperatures of the states A and B, respectively. It is most likely that
Let Cv and Cp denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?
70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
The figure shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.
The molar heat capacity for the process shown in the figure is
One mole of gas expands obeying the relation as shown in the P-V diagram. The maximum temperature in this process is equal to ______.
