객관식
What volume will 4.70 g of nitrogen gas (N₂) occupy at STP?
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7. Gases
The Ideal Gas Law: Molar Mass
객관식
A gas has a density of 0.890 g/L at 1.00 atm and 75.0 °C. What is its molar mass in g/mol?
A
18.0
B
28.9
C
44.0
D
22.0
검증된 단계별 안내1
Identify the known variables: density (d) = 0.890 g/L, pressure (P) = 1.00 atm, temperature (T) = 75.0 °C. Convert the temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
Recall the ideal gas law equation: \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
Express the number of moles \(n\) in terms of mass and molar mass: \(n = \frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass.
Rewrite the ideal gas law in terms of density \(d = \frac{m}{V}\) by substituting \(n = \frac{m}{M}\) into \(PV = nRT\), resulting in \(P = \frac{dRT}{M}\), and then solve for molar mass \(M\) as \(M = \frac{dRT}{P}\).
Plug in the values for density \(d\), gas constant \(R\) (use \(0.0821\ \text{L}\cdot\text{atm}/\text{mol}\cdot\text{K}\)), temperature \(T\) in Kelvin, and pressure \(P\) to calculate the molar mass \(M\).
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