The vessel containing 2 g of helium burst at 400 ° C. What is the maximum amount of nitrogen

| March 25, 2021 | education

The vessel containing 2 g of helium burst at 400 ° C. What is the maximum amount of nitrogen that can be stored in such a container at 30 ° C and at five times the strength of the sand?

Data: mHe is the mass of helium (mHe = 2 g); THe – abs. helium temperature (THe = 673 K (400 ºС)); TN2 – abs. nitrogen temperature (TN2 = 303 K (30 ºС)); РN2 / РHe – ratio of gas pressures, safety factor (РN2 / РHe = 1/5).

Const: МНе – molar mass of helium (МНе ≈ 4 g / mol); МN2 – molar mass of nitrogen (МN2 ≈ 28 * 10-3 kg / mol).

Since the volume of the vessel for gases is constant, the maximum amount of nitrogen is determined from the equality: mHe * R * THe / (МНе * РHe) = V = mN2 * R * TN2 / (МN2 * РN2) from where we express: mN2 = МN2 * РN2 * mHe * R * THe / (MHe * PHe * R * TN2) = MN2 * PH2 * mHe * THe / (MHe * PHe * TN2).

Let’s calculate: mN2 = МN2 * РN2 * mHe * THe / (МНе * РHe * TN2) = 28 * 2 * 673 / (5 * 4 * 303) ≈ 6.22 g.

Answer: The vessel can store 6.22 g of nitrogen.



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