Answer

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**Hint:**Ideal gas equation is an equation of hypothetical gas. It helps in telling us the behaviour of gases under several conditions.

-Mole concept gives us the relation between the number of moles, weight and the molar mass of a given compound.

**Formula used:**

$PV=nRT$

Where, $P$ is the pressure

$V$ is the volume

$n$ is the number of moles

$R$ is the universal gas constant

$T$ is the temperature

The weight can be calculated by the product of the number of moles and molar mass

$w=n\times m$

$w$ Is the weight

$m$ Is the molar mass

$n$ Is the number of moles

**Complete step by step answer:**

According to the ideal gas equation:

The product of pressure and volume gives us the relation between the product of gas constant and temperature.

Here, it is given that the volume of the helium gas in balloon is $1\times {{10}^{5}}$

The given temperature is $268K$

The given pressure is $2\times {{10}^{-3}}$

$PV=nRT$

Where, $P$ is the pressure

$n$ Is the number of moles

$V$ Is the volume

$T$ Is the temperature

$R$ Is the gas constant

Now, substituting the values in above formula we get,

$2\times {{10}^{-3}}\times {{10}^{5}}=n\times 0.0821\times 268$

On further solving ,

$n=9.08$ $mol$

The weight can be calculated by the product of the number of moles and molar mass

$w=n\times m$

Where, $n$ is the number of moles

$w$ is the weight

$m$ is the molar mass

The molar mass of helium is $4g$

On substituting the above value in this formula we get,

$w=9.08\times 4$

$w=36.32g$

**Therefore, the weight of helium to fully inflate the balloon is $36.32g$.**

**Note:**

-The number of moles is defined as the weight per molar mass of the given compound.

-Ideal gas equation tells the behaviour of gases under many conditions.

-Here, the value of universal gas constant is $0.0821$ $latmmo{{l}^{-1}}{{K}^{-1}}$

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