Answer:
At 268.82°C volume occupied by nitrogen is 10 liters at pressure of 900 torr.
Explanation:
Given:
Volume of a sample of nitrogen = 5.50 liters
Pressure = 900 torr
Temperature = 25°C
To find the temperature at which the nitrogen will occupy 10 liters volume at same pressure.
Solution:
Since the pressure is kept constant, so we can apply the temperature-volume law also called the Charles Law.
Charles Law states that the volume of a gas held at constant pressure is directly proportional to the temperature of the gas in Kelvin.
Thus, we have :
[tex]V[/tex] ∝ [tex]T[/tex]
[tex]\frac{V}{T}=k[/tex]
where [tex]k[/tex] is a constant.
For two samples of gases, the law can be given as:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
From the data given:
[tex]V_1=5.5\ l[/tex]
[tex]T_1=25\ \°C =(273+25)K= 298 K[/tex]
[tex]V_2=10\ l[/tex]
We need to find [tex]T_2[/tex].
Plugging in values in the formula.
[tex]\frac{5.5}{298}=\frac{10}{T_2}[/tex]
Multiplying both sides by [tex]T_2[/tex].
[tex]T_2\times\frac{5.5}{298}=\frac{10}{T_2}\times T_2[/tex]
[tex]\frac{5.5}{298}T_2={10}[/tex]
Multiplying both sides by [tex]\frac{298}{5.5}[/tex]
[tex]\frac{298}{5.5}\times\frac{5.5}{298}T_2=\frac{10\times 298}{5.5}[/tex]
[tex]T_2=541.82\ K[/tex]
[tex]T_2=541.82\ K-273\ K = 268.82\°C[/tex]
Thus, at 268.82°C volume occupied by nitrogen is 10 liters at pressure of 900 torr.
The temperature at which the gas will occupy 10 L is 268.8 °C
We'll begin by listing out what was given from the question. This includes:
Initial volume (V₁) = 5.5 L
Initial temperature (T₁) = 25 °C = 25 + 273 = 298 K
Final volume (V₂) = 10 L
Pressure = constant
Using the Charles' law equation, we can obtain the new temperature of the gas as illustrated below:
[tex]\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \\\\\frac{5.5}{298} = \frac{10}{T_{2}} \\\\[/tex]
Cross multiply
5.5 × T₂ = 298 × 10
5.5 × T₂ = 2980
Divide both side by 5.5
[tex]T_{2} = \frac{2980}{5.5}\\\\[/tex]
T₂ = 541.8
Subtract 273 to express in degree celsius (°C)
T₂ = 541.8 – 273
Therefore, the temperature at which the gas will occupy 10 L is 268.8 °C
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