A sample of carbon dioxide gas at a pressure of 1.07 atm and a temperature of 166 °C, occupies a volume of 686 mL. If the gas is heated at constant pressure until its volume is 913 mL, the temperature of the gas sample will be ? °C.
A very important thing to remember is that the temperature of the gas must be expressed in Kelvin. In other words, you must always work with the absolute temperature of a gas.
So, start by converting the temperature of the gas to Kelvin by using
You will have
The volume of the gas will increase as temperature increases and decrease as temperature decreases. Mathematically, this can be written as
Here
Plug in your values to find
Finally, convert this to degrees Celsius
The answer is rounded to three sig figs.
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To find the final temperature of the gas sample, we can use the combined gas law equation:
[ \frac{{P_1 \cdot V_1}}{{T_1}} = \frac{{P_2 \cdot V_2}}{{T_2}} ]
where: ( P_1 = 1.07 , \text{atm} ) (initial pressure) ( V_1 = 686 , \text{mL} ) (initial volume) ( T_1 = 166 , \text{°C} ) (initial temperature) ( P_2 = 1.07 , \text{atm} ) (final pressure, constant pressure) ( V_2 = 913 , \text{mL} ) (final volume) ( T_2 ) is the final temperature we're solving for.
Rearranging the equation to solve for ( T_2 ), we get:
[ T_2 = \frac{{P_2 \cdot V_2 \cdot T_1}}{{P_1 \cdot V_1}} ]
Plugging in the values, we get:
[ T_2 = \frac{{1.07 , \text{atm} \times 913 , \text{mL} \times 166 , \text{°C}}}{{1.07 , \text{atm} \times 686 , \text{mL}}} ]
[ T_2 \approx 344.7 , \text{°C} ]
So, the temperature of the gas sample will be approximately ( 344.7 , \text{°C} ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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