To determine the number of moles of gas in the given scenarios, we can use the Ideal Gas Law, which is expressed as:
\[ PV = nRT \]
where:
- \( P \) = pressure in atm,
- \( V \) = volume in liters,
- \( n \) = number of moles,
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol)),
- \( T \) = temperature in Kelvin.
Question 1:
For the first scenario, since we are asked how much gas we have in terms of moles at STP:
Standard conditions are \( P = 1 , \text{atm} \) and \( T = 273 , \text{K} \).
The volume of 1 mole of an ideal gas at STP is 22.4 L.
To find the number of moles (\( n \)): \[ n = \frac{V}{22.4 , \text{L/mol}} = \frac{44.8 , \text{L}}{22.4 , \text{L/mol}} = 2.0 , \text{moles} \]
Answer for Question 1:
2.0 moles
Question 2:
For the second scenario where the gas occupies 10.5 L at a pressure of 1.2 atm and a temperature of 298 K:
Using the ideal gas law: \[ n = \frac{PV}{RT} \]
Substituting the values:
- \( P = 1.2 , \text{atm} \)
- \( V = 10.5 , \text{L} \)
- \( R = 0.0821 , \text{L·atm/(K·mol)} \)
- \( T = 298 , \text{K} \)
Calculating the number of moles: \[ n = \frac{(1.2 , \text{atm})(10.5 , \text{L})}{(0.0821 , \text{L·atm/(K·mol)})(298 , \text{K})} \]
Calculating the denominator: \[ 0.0821 \times 298 \approx 24.4758 \]
Now substituting back in: \[ n = \frac{12.6}{24.4758} \approx 0.515 , \text{mol} \]
Answer for Question 2:
0.52 mol