Advertisements
Advertisements
प्रश्न
Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure
Advertisements
उत्तर १
Volume of the room, V = 25.0 m3
Temperature of the room, T = 27°C = 300 K
Pressure in the room, P = 1 atm = 1 × 1.013 × 105 Pa
The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T) can be written as:
PV = kBNT
Where,
KB is Boltzmann constant = 1.38 × 10–23 m2 kg s–2 K–1
N is the number of air molecules in the room
`:. N = (PV)/(k_BT)`
`= (1.013xx10^5xx25)/(1.38xx10^(-23)xx300) = 6.11 xx 10^(26)` molecules
Therefore, the total number of air molecules in the given room is 6.11 × 1026.
उत्तर २
Here, Volume of room, `V= 25.0 m^3`, temperature, `T = 27 ^@C = 300 K` and
Pressure, `P = 1 "atm" = 1.01 xx 10^5 Pa`
According to gas equation, `PV = muRT = muN_A.k_BT`
Hence, total number of air molecules in the volume of given gas
`N = mu.N_A = PV/K_BT`
`:. N = (1.01 xx 10^5 xx25.0)/((1.38 xx 10^(-23))xx300) = 6.1 xx 10^(26)`
संबंधित प्रश्न
Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres
The figure shows the plot of PV/T versus Pfor 1.00×10–3 kg of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true: T1 > T2 or T1 < T2?
(c) What is the value of PV/T where the curves meet on the y-axis?
(d) If we obtained similar plots for 1.00 ×10–3 kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot)? (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u, R = 8.31 J mo1–1 K–1.)
Oxygen is filled in a closed metal jar of volume 1.0 × 10−3 m3 at a pressure of 1.5 × 105Pa and temperature 400 K. The jar has a small leak in it. The atmospheric pressure is 1.0 × 105 Pa and the atmospheric temperature is 300 K. Find the mass of the gas that leaks out by the time the pressure and the temperature inside the jar equalise with the surrounding.
50 m3 of saturated vapour is cooled down from 30°C to 20°C. Find the mass of the water condensed. The absolute humidity of saturated water vapour is 30 g m−3 at 30°C and 16 g m−3 at 20°C.
Give reasons for the following:
Gas fills the vessel completely in which it is kept.
A gas occupies 500 cm3 at a normal temperature. At what temperature will the volume of the gas be reduced by 20% of its original volume, the pressure is constant?
Name or state the following:
An equation used in chemical calculations which gives a simultaneous effect of changes of temperature and pressure on the volume of a given mass of dry gas
Name or state the following:
The standard pressure of a gas in cm. of mercury corresponding to one atmospheric pressure.
Gases exert pressure on the walls of the container because the gas molecules ______
Estimate the average thermal energy of a helium atom at room temperature (27 °C).
Estimate the average thermal energy of a helium atom at the temperature on the surface of the Sun (6000 K).
Which of the following diagrams (Figure) depicts ideal gas behaviour?
 (a) |
 (b) |
 (c) |
 (d) |
Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197g mole–1.
The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is ______.
P ∝ T at constant volume is the statement of ______.
Two tanks of equal volume contain equal mass of oxygen and nitrogen at 127°C. Find the ratio of pressure in two tanks.
