Question

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A gas is to be filled from a tank of capacity 10,000 litres into cylinders each having capacity of 10 litres. The condition of the gas in the tank is as follows :
(a) pressure inside the tank is 800 mm of Hg.
(b) temperature inside the tank is -3°C.
When the cylinder is filled, the pressure gauge reads 400 mm of Hg and the temperature is 270 K. Find the number of cylinders required to fill the gas.​

Answer 1

Topic :-

Gas Equation

Given :-

A gas is to be filled from a tank of capacity 10,000 litres into cylinders each having capacity of 10 litres. The condition of the gas in the tank is as follows :

(a) pressure inside the tank is 800 mm of Hg.

(b) temperature inside the tank is -3°C.

When the cylinder is filled, the pressure gauge reads 400 mm of Hg and the temperature is 270 K.

To Find :-

The number of cylinders required to fill the gas.​

Formula to be Used :-

PV = nRT

where

P = Pressure inside container

V = Volume of container

n = Number of moles of gas

R = Universal Gas Constant

T = Temperature inside container

Solution :-

To solve this type of question, first we calculate number of moles present in containers and then calculate number of container accordingly.

It is given that tank has,

V = 10, 000 litres

P = 800 mm of Hg

T = -3 °C or

T = (273 - 3) K = 270 K

Calculating number of moles present in tank,

PV = nRT

800 × 10000 = nR × 270

$n=\dfrac{800 \times 10000}{270 \times R}$

$n=\dfrac{800000}{27R}$

It is given that cylinder has,

V = 10 litres

P = 400 mm of Hg

T = 270 K

Calculating number of moles present in a cylinder,

PV = n'RT

400 × 10 = nR × 270

$n'=\dfrac{400 \times 10}{270 \times R}$

$n'=\dfrac{400}{27R}$

Calculating number of moles,

Let number of cylinders rerquired to fill the gas be 'x'.

As number of moles should be equal inside tank and 'x' number of cylinders.

So, moles of tank is equal to 'x' times of moles of cylinders.

n = xn'

$\dfrac{800000}{27R}=x\times \dfrac{400}{27R}$

$x= \dfrac{800000}{400}$

$x = 2000$

Answer :-

So, total number of cylinders required to fill the gas is 2000.

Answer 2

= 2022 cylinders

Question solved✅