Answer:
1.11 atm
(P, T)
2.83 atm
0.740 g
0.179 g/L, 0.158 g/L
N₂
Explanation:
<em>One mole of an ideal gas is sealed in a 22.4-L container at a pressure of 1 atm and a temperature of 273 K. The temperature is then increased to 304 K, but the container does not expand. What will the new pressure be?</em>
Assuming ideal behavior, we can calculate the new pressure (P₂) using Gay-Lussac's law.
![\frac{P_{1}}{T_{1}} =\frac{P_{2}}{T_{2}} \\P_{2}=\frac{P_{1}}{T_{1}}.T_{2}=\frac{1atm}{273K} .304K=1.11atm](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%7D%7BT_%7B1%7D%7D%20%3D%5Cfrac%7BP_%7B2%7D%7D%7BT_%7B2%7D%7D%20%5C%5CP_%7B2%7D%3D%5Cfrac%7BP_%7B1%7D%7D%7BT_%7B1%7D%7D.T_%7B2%7D%3D%5Cfrac%7B1atm%7D%7B273K%7D%20.304K%3D1.11atm)
<em>The most appropriate formula for solving this problem includes only which variables?</em>
Gay-Lussac's law includes pressure (P) and absolute temperature (T).
<em>Q2) A sample of nitrogen gas in a 1.69-L container exerts a pressure of 1.37 atm at 17 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 327 °C?
</em>
Initially the system is at 17°C (290 K) and the temperature is raised to 327°C (600 K). We can calculate the new pressure using Gay-Lussac's law.
![\frac{P_{1}}{T_{1}} =\frac{P_{2}}{T_{2}} \\P_{2}=\frac{P_{1}}{T_{1}}.T_{2}=\frac{1.37atm}{290K} .600K=2.83atm](https://tex.z-dn.net/?f=%5Cfrac%7BP_%7B1%7D%7D%7BT_%7B1%7D%7D%20%3D%5Cfrac%7BP_%7B2%7D%7D%7BT_%7B2%7D%7D%20%5C%5CP_%7B2%7D%3D%5Cfrac%7BP_%7B1%7D%7D%7BT_%7B1%7D%7D.T_%7B2%7D%3D%5Cfrac%7B1.37atm%7D%7B290K%7D%20.600K%3D2.83atm)
<em>Q3) A gas mixture with a total pressure of 770 mmHg contains each of the following gases at the indicated partial pressures: 120 mmHg CO₂, 227mmHg Ar, and 190 mmHg O₂. The mixture also contains helium gas
.</em>
What mass of helium gas is present in a 14.0-L sample of this mixture at 282 K?
First, we have to calculate the pressure of Helium. We know that the total pressure is the sum of partial pressures.
Ptotal = pCO₂ + pAr + pO₂ + pHe
pHe = Ptotal - pCO₂ - pAr - pO₂
pHe = 770mmHg - 120mmHg - 227mmHg - 190mmHg=233mmHg
We can calculate the moles of Helium using the ideal gas equation.
![P.V=n.R.T\\n=\frac{P.V}{R.T} =\frac{233mmHg.14.0L}{(0.08206atm.L/mol.K).282K} .\frac{1atm}{760mmHg} =0.185mol](https://tex.z-dn.net/?f=P.V%3Dn.R.T%5C%5Cn%3D%5Cfrac%7BP.V%7D%7BR.T%7D%20%3D%5Cfrac%7B233mmHg.14.0L%7D%7B%280.08206atm.L%2Fmol.K%29.282K%7D%20.%5Cfrac%7B1atm%7D%7B760mmHg%7D%20%3D0.185mol)
The molar mass of He is 4.00g/mol.
![0.185mol.\frac{4.00g}{mol} =0.740g](https://tex.z-dn.net/?f=0.185mol.%5Cfrac%7B4.00g%7D%7Bmol%7D%20%3D0.740g)
<em>Calculate the density of oxygen, O₂, under each of the following conditions:
</em>
- <em>1.00 atm and 35.0 ∘C
</em>
<em>
Express your answers numerically in grams per liter. Enter the density at STP first and separate your answers by a comma.</em>
<em />
STP stands for Standard Temperature and Pressure. The standard temperature is 273 K and the standard pressure is 1 atm.
We can calculate the density using the following expression:
![\rho=\frac{P.M}{R.T} =\frac{1.00atm.4.00g/mol}{(0.08206atm.L/mol.K).273K} =0.179 g/L](https://tex.z-dn.net/?f=%5Crho%3D%5Cfrac%7BP.M%7D%7BR.T%7D%20%3D%5Cfrac%7B1.00atm.4.00g%2Fmol%7D%7B%280.08206atm.L%2Fmol.K%29.273K%7D%20%3D0.179%20g%2FL)
<em>At 1.00 atm and 35.0 °C (308 K)</em>
![\rho=\frac{P.M}{R.T} =\frac{1.00atm.4.00g/mol}{(0.08206atm.L/mol.K).308K} =0.158 g/L](https://tex.z-dn.net/?f=%5Crho%3D%5Cfrac%7BP.M%7D%7BR.T%7D%20%3D%5Cfrac%7B1.00atm.4.00g%2Fmol%7D%7B%280.08206atm.L%2Fmol.K%29.308K%7D%20%3D0.158%20g%2FL)
<em>To identify a diatomic gas (X₂), a researcher carried out the following experiment: She weighed an empty 4.1-L bulb, then filled it with the gas at 2.00 atm and 24.0 ∘C and weighed it again. The difference in mass was 9.5 g . Identify the gas. Express your answer as a chemical formula.</em>
We will look for the molar mass of the compound using the ideal gas equation.
![P.V=n.R.T=\frac{m}{M} .R.T\\M=\frac{m.R.T}{P.V} =\frac{9.5g \times (0.08206atm.L/mol.K)\times 297K }{2.00atm \times 4.1L} =28g/mol](https://tex.z-dn.net/?f=P.V%3Dn.R.T%3D%5Cfrac%7Bm%7D%7BM%7D%20.R.T%5C%5CM%3D%5Cfrac%7Bm.R.T%7D%7BP.V%7D%20%3D%5Cfrac%7B9.5g%20%5Ctimes%20%280.08206atm.L%2Fmol.K%29%5Ctimes%20297K%20%7D%7B2.00atm%20%5Ctimes%204.1L%7D%20%3D28g%2Fmol)
If the molar mass of X₂ is 28 g/mol, the molar mass of X is 14 g/mol. Then, X is nitrogen and X₂ is N₂.