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Question: The density of liquid nitrogen is \(0.807gm/{L^3}\) . If a person accidentally swallowed a \(0.28mL\...

The density of liquid nitrogen is 0.807gm/L30.807gm/{L^3} . If a person accidentally swallowed a 0.28mL0.28mL drop of liquid nitrogen. What volume of nitrogen gas would be evolved in their body at 100kPa100kPa and 27∘C27^\circ C?

Explanation

Solution

We know that liquid nitrogen exists in very low temperatures (negative temperatures). Standard liquid nitrogen exists at −195.7∘C - 195.7^\circ C . It is a colorless and low viscous liquid which is generally used as a coolant. To evaluate the given condition in the question, we will use ideal gas law because this law gives the general equation which approximates the behavior of gases under different conditions.

Complete step by step answer:
Given:
Density of liquid nitrogen = 0.807gm/L30.807gm/{L^3}
Mass of liquid nitrogen swallowed (m) = 0.28mL0.28mL
Molar mass of liquid nitrogen (M) = 28gm/mol28gm/mol
Temperature = 27+273=300K27 + 273 = 300K
Pressure = 100kPa100kPa= 9.869×10−6atm9.869 \times {10^{ - 6}}atm
We know that the expression for ideal gas law is given as,
PV=nRTPV = nRT
Where n=mM=mass of the compoundmolecular mass of the compoundn = \dfrac{m}{M} = \dfrac{{{\text{mass of the compound}}}}{{{\text{molecular mass of the compound}}}}
∴V=nRTP\therefore V = \dfrac{{nRT}}{P}
⇒V=mRTMP\Rightarrow V = \dfrac{{mRT}}{{MP}}
Now we can substitute the known values we get,
⇒V=0.28×0.0821×30028×9.869×10−6\Rightarrow V = \dfrac{{0.28 \times 0.0821 \times 300}}{{28 \times 9.869 \times {{10}^{ - 6}}}}
On simplification we get,
⇒V=2.5L3\Rightarrow V = 2.5{L^3}
Hence, the volume of nitrogen gas which will be liberated inside the human body is 2.5L32.5{L^3} .
From this evaluation we can see that liquid nitrogen in small amounts when evolves as gas the volume is much higher than the actual volume of liquid nitrogen. Nitrogen gas under lower temperature exists as liquid nitrogen. This liquid nitrogen boils immediately when the temperature increases. Even at room temperature the liquid nitrogen readily vaporizes as gas.

Note:
We must remember that the ideal gases law came into existence because the different gases when compressed or solidified show different properties. The properties in its different form changes for some elements while some elements also retain their properties in different states. Thus, in case of nitrogen in liquid state the volume is less and that in gases state is more. Though consuming liquid nitrogen is not preferable as even a small amount of liquid boils readily at room temperature and in the stomach it can create a hole due to the gases evolved and in the human body there is no space for gas to escape.