To analyze the behavior of the fixed quantity of gas under various conditions, we can use the Ideal Gas Law, which is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas (in atm)
- \( V \) = volume of the gas (in liters)
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature of the gas (in Kelvin)
First, we need to convert the given temperature from °C to Kelvin:
\[ T(K) = T(°C) + 273.15 = 21 + 273.15 = 294.15 , K \]
Next, we convert the pressure from torr to atm:
\[ P(atm) = \frac{P(torr)}{760} = \frac{760, torr}{760} = 1 , atm \]
Now, we can plug the values of \( P \), \( V \), and \( T \) into the Ideal Gas Law to find \( n \) (the number of moles of gas):
\[ PV = nRT \]
Substituting the known values:
\[ (1, atm)(5.32, L) = n(0.0821, L·atm/(K·mol))(294.15, K) \]
Now, calculate \( n \):
\[ 5.32 = n(0.0821)(294.15) \]
Calculating the right-hand side:
\[ 0.0821 \times 294.15 \approx 24.228 \]
Now, the equation becomes:
\[ 5.32 = n(24.228) \]
To find \( n \):
\[ n = \frac{5.32}{24.228} \approx 0.22 , moles \]
Summary
- Pressure: 760 torr → 1 atm
- Temperature: 21 °C → 294.15 K
- Volume: 5.32 L
- Moles of gas: approximately 0.22 moles
With this information, we can assess how the gas will behave under different pressures or volumes if needed. If you have any specific scenario or additional calculations in mind, please let me know!
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