If a gas occupies a volume of 400cm\(^3\) at a temperature of 400K and a pressure of 1 atm, at what temperature and pressure would its volume be 200cm\(^3\)?
To determine the correct conditions, we use the Combined Gas Law, which relates the pressure, volume, and temperature of a fixed amount of gas:
\(\frac{P\(_1\)V\(_1\)}{T\(_1\)}\) = \(\frac{P\(_2\)V\(_2\)}{T\(_2\)}\)
Given:
V\(_1\) = 400 cm\(^3\) , T\(_1\) = 400 K , P\(_1\) = 1 atm
V\(_2\) = 200 cm\(^3\) , T\(_2\) = ? , P\(_2\) = ?
We need to find which pair of pressure and temperature satisfies the equality
P\(_1\)V\(_1\)/T\(_1\) = P\(_2\)V\(_2\)/T\(_2\)
First, calculate the initial constant:
\(\frac{1 atm . 400cm{^3}}{400K}\) = 1
Now, test Option C:
P\(_2\) = 1 atm
V\(_2\) = 200cm\(^3\)
T\(_2\) = 200 K
\(\frac{1 atm . 200cm{^3}}{200K}\) = 1
Options A, B and D will not give you 1.
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