To determine the Celsius temperature of 1.50 moles of ammonia contained in a 10.0-liter vessel under a pressure of 2.0 atm, we can use the Ideal Gas Law, which is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \( T \) = temperature (in Kelvin)
- First, let's rearrange the Ideal Gas Law to solve for temperature \( T \):
\[ T = \frac{PV}{nR} \]
- Now, plug in the values:
- \( P = 2.0 \) atm
- \( V = 10.0 \) liters
- \( n = 1.50 \) moles
- \( R = 0.0821 \) L·atm/(K·mol)
- Calculate \( T \):
\[ T = \frac{(2.0 , \text{atm}) \times (10.0 , \text{L})}{(1.50 , \text{mol}) \times (0.0821 , \text{L·atm/(K·mol)})} \]
\[ T = \frac{20.0}{1.2315} \approx 16.24 , \text{K} \]
- Convert temperature \( T \) from Kelvin to Celsius:
\[ T_C = T - 273.15 \]
\[ T_C = 16.24 - 273.15 \approx -256.91 , °C \]
However, it appears there might be values calculated incorrectly in the earlier steps.
Let's cross-verify the calculations:
After re-evaluating, if we multiply everything correctly, we should have:
\[ T = \frac{(2.0)(10)}{(1.50)(0.0821)} = \frac{20}{0.12315} \approx 162.0 , K \]
To convert kelvin to Celsius:
\[ T_C = 162.0 - 273.15 \approx -111.15 , °C \]
For accuracy:
With this correction, looking at the values provided (not that they would correctly apply), it means re-check the steps and obtain accordingly instead of wrong mentions.
Let's clearly re-evaluate:
\[ T_C = \frac{(2.0)(10)}{(1.50)(0.0821)} \approx \]
\[ 20 = 20.00 / \approx 2.0 + 162.0 ; \]
So, as an overview of the data, it rounds: At Kelvin, you derive approx. 162°C for the estimation.
Thus therefore from available values, based on chosen constraints look through match, good around of selection:
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