The density of a gas at N.T.P.is 'ρ'. Keeping the pressure constant (i.e. 760 mm Hg), the 3 density of the gas will become at a temperature of __________ °K

ANS:C - 400°

To find the new density of the gas at a different temperature while keeping the pressure constant, we can use the ideal gas law: 𝑃𝑉=𝑛𝑅𝑇PV=nRT Where:

• 𝑃P is the pressure (constant, in this case, 760 mm Hg)
• 𝑉V is the volume
• 𝑛n is the number of moles (assumed constant)
• 𝑅R is the gas constant
• 𝑇T is the temperature (in Kelvin)

The density (𝜌ρ) of the gas is related to its molar mass (𝑀M) and the volume of the gas (𝑉V): 𝜌=𝑚𝑉=𝑀⋅𝑛𝑉ρ=Vm​=VM⋅n​ Since 𝑛/𝑉n/V is constant (from the ideal gas law), we can say that: 𝜌1=𝜌2ρ1​=ρ2​ Where 𝜌1ρ1​ is the initial density at N.T.P. and 𝜌2ρ2​ is the density at the new temperature. Now, according to the ideal gas law: 𝑃𝑉𝑇=constantTPV​=constant Given that pressure (𝑃P) is constant and the volume (𝑉V) is constant, we can say: 𝑇1𝑇2=𝑉1𝑉2T2​T1​​=V2​V1​​ Since 𝑉1=𝑉2V1​=V2​ (volume is constant), we have: 𝑇1=𝑇2T1​=T2​ This means that the temperature in Kelvin remains the same. So, regardless of the temperature, if the pressure is kept constant, the density of the gas will remain the same. Therefore, the correct answer is none of the options provided.