Gas Law Equation: Determining the Noble Gas in a Syringe

What noble gas is present in the syringe based on the given data?

The noble gas in the syringe is Neon (Ne).

To determine which noble gas is in the syringe, we can use the ideal gas law equation: PV = nRT

Ideal Gas Law Equation:

PV = nRT

Where:

  • P = pressure of the gas (in atm)
  • V = volume of the gas (in liters)
  • n = number of moles of gas
  • R = ideal gas constant (0.0821 L·atm/mol·K)
  • T = temperature of the gas (in Kelvin)

First, we need to convert the given pressure of 3.20 atm to Pascals (Pa). Since 1 atm = 101325 Pa, we have:

P = 3.20 atm × 101325 Pa/atm = 324960 Pa

Next, we convert the volume of the gas from milliliters (mL) to liters (L). Since 1 L = 1000 mL, we have:

V = 75.0 mL × 1 L/1000 mL = 0.075 L

The mass of the syringe increases by 0.202 g, which indicates the mass of the noble gas added. To determine the number of moles of the noble gas, we can use the ideal gas law rearranged to solve for n:

n = (PV) / (RT)

Substituting the given values:

n = (324960 Pa) × (0.075 L) / [(0.0821 L·atm/mol·K) × (20.0 + 273 K)]

n = 24513.6 Pa·L / (8.314 L·Pa/mol·K × 293 K)

n ≈ 9.28 mol

Since 1 mole of any noble gas has the same mass, we can determine the noble gas by comparing the number of moles to their molar masses. The noble gas with a molar mass closest to 9.28 g/mol is Neon (Ne), which has a molar mass of 20.18 g/mol.

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