Answer: The pressure will be equal to 0.19 atm.
Explanation:
The Ideal Gas Equation states the relationship among the pressure, temperature, volume, and number of moles of a gas.
The equation is:
[tex]PV=nRT[/tex]
where P = pressure in atm
V = volume in L
n = numbers of moles of gas in mol
R = universal gas constant = 0.08206 [tex]\frac{L-atm}{mol - K}[/tex]
T = temperature in K
Based on the problem,
mass of O2 = 1.0 g
V = 4.00 L
T = 293 K
mol of O2 = ?
P = ?
We need to calculate the moles of O2 before we can use the Ideal Gas Equation. To solve the number of moles, we use the equation:
[tex]no. of moles = \frac{given\ mass\ (in\ grams) }{molar\ mass\ (in\ \frac{grams}{mole}) }[/tex]
The molar mass of O2 is 32 g/mol, therefore,
[tex]no. of moles = \frac{1.0g}{32\frac{g}{mol} }[/tex]
no. of moles of O2 = 0.03125 mol.
Now we substitute the values into the Ideal Gas equation:
[tex]P(4.00L) = (0.03125 mol)(0.08206\frac{L-atm}{mol-K} )(293K)[/tex]
Solving for P, we will get
[tex]P=\frac{(0.03125mol)(0.08206\frac{L-atm}{mol-K})(293K) }{4.00L} \\\\P= 0.1878 atm.[/tex]
In correct significant figures, P is equal to 0.19 atm.
