Liquefied natural gas(LNG) is mainly methane. A $10.0$ $m^{3}$ tank is constructed to store LNG at $- 164^{o}$ C and $1$ atm pressure, under which conditions its density is $416$ $k g / m^{3}$ . The volume(in $m^{3}$ ) of a storage tank capable of holding the same mass of LNG as a gas, at $27^{o}$ C and $1.642$ atm pressure, is?

Open in App

Solution

Given volume $= 10.0 m^{3}$
density $= 416$ kg $/ m^{3} = 416 \times 10^{3} g / m^{3}$
$P = 1642$
$T = 300$ k

Mass $=$ density $\times$ volume

$= 416 \times 10^{3} \times 10$

$= 416 \times 10^{4}$

No. of moles of methane $= \frac{m a s s}{m o l a r m a s s} = \frac{416 \times 10^{4}}{16}$

$= 26 \times 10^{4}$ moles

Using the ideal gas equation

$p V = n R T$

$V = \frac{n R T}{P} = \frac{26 \times 10^{4} \times 0.082 \times 300}{1.642}$

$V = 3875.89 \times 10^{3}$

$V \approx 3900$

$= 39 \times 10^{5}$ .

Suggest Corrections

Similar questions

Q. A heating coil is immersed in a 100 g sample of

H_{2} O (l)

at 1 atm and

100^{\circ} C

in a closed vessel. In this heating process,

60 %

of the liquid is converted into a gas at a constant pressure of 1 atm. Densities of liquid and gaseous water under these conditions are

1000 kg / m^{3}

and

0.60 kg / m^{3}

respectively. The magnitude of the work done for this process is: (Take 1 atm

= 10^{5} Pa

)

Q. If the density of a certain gas at 30 degree C and 768 torr is 1.35 kg/m3 it's density at STP would be 1. 1.48 kg/m3 2. 1.58 kg/m3 3. 1.25 kg/m3 4. 1.4 kg/m3

The density of vapour of a substance (X) at 1 atm pressure and 500 K is 0.8 $\frac{k g}{m^{3}}$ . The vapour effuses through a small hole at a rate of $\frac{4}{5}$ times slower than oxygen under the same condition. What is the compressibility factor (Z) of the vapour?

If the densities of a gas at sea level at 0 celsius is 1.29 kg/m³ at 1 atm. ,what will be its molar mass?

Q. If the density of a certain gas at 30^.c and 768 torr is 1.35kg/m³ its density at STPwould be
(1) 1.48kg/m³
(2) 1.58kg/m3
(3) 1.25kg/m³
(4) 1.4kg/m³

Join BYJU'S Learning Program

Liquefied natural gas(LNG) is mainly methane. A 10.0 m3 tank is constructed to store LNG at −164oC and 1 atm pressure, under which conditions its density is 416 kg/m3. The volume(in m3) of a storage tank capable of holding the same mass of LNG as a gas, at 27oC and 1.642 atm pressure, is?

Given volume=10.0m3density=416 kg/m3=416×103g/m3P=1642T=300kMass=density × volume=416×103×10=416×104No. of moles of methane =massmolar mass=416×10416=26×104 molesUsing the ideal gas equationpV=nRTV=nRTP=26×104×0.082×3001.642V=3875.89×103V≈3900=39×105.