Question

the ideal gas law
four quantities describe the state of a gas: pressure, volume, temperature, and # of moles (quantity).
combine all 3 laws!

replace the \\( \propto \\) with a constant, \\( r \\), and you get:

the ideal gas law is an equation of state.
\\( r = 0.08206 \mathrm { l } \cdot \mathrm { atm } / \mathrm { mol } \cdot \mathrm { k } \\) also expressed
as \\( 0.08206 \mathrm { l } \mathrm { atm } \mathrm { mol } ^ { - 1 } \mathrm { k } ^ { - 1 } \\)

useful only at low pressures and high temperatures!
guaranteed points on the ap exam!

these next exercises can all be solved with the ideal gas law, but, you can use another if you like!

exercise 8 ideal gas law i
a sample of hydrogen gas \\( ( \mathrm { h } _ { 2 } ) \\) has a volume of \\( 8.56 \mathrm { l } \\) at a temperature of \\( 0 ^ { \circ } \mathrm { c } \\) and a pressure of
\\( 1.5 \mathrm { atm } \\). calculate the moles of \\( \mathrm { h } _ { 2 } \\) molecules present in this gas sample.

exercise 9 which gas law?
suppose we have a sample of ammonia gas with a volume of \\( 3.5 \mathrm { l } \\) at a pressure of \\( 1.68 \mathrm { atm } \\). the gas is
compressed to a volume of \\( 1.35 \mathrm { l } \\) at a constant temperature. use the ideal gas law to calculate the final
pressure.

exercise 10 which gas law?
a sample of methane gas that has a volume of \\( 3.8 \mathrm { l } \\) at \\( 5 ^ { \circ } \mathrm { c } \\) is heated to \\( 86 ^ { \circ } \mathrm { c } \\) at constant pressure. calculate its
new volume.

gases

Explanation:

Step1: Convert temperatures to Kelvin

For Exercise 10, convert \(T_1 = 5^{\circ}C\) to \(T_1=5 + 273=278\space K\) and \(T_2 = 86^{\circ}C\) to \(T_2=86 + 273 = 359\space K\).

Step2: Apply Charles's Law (\(\frac{V_1}{T_1}=\frac{V_2}{T_2}\))

Given \(V_1 = 3.8\space L\), \(T_1 = 278\space K\), \(T_2=359\space K\). Rearrange for \(V_2\): \(V_2=\frac{V_1T_2}{T_1}\).
Substitute values: \(V_2=\frac{3.8\times359}{278}\).
Calculate \(3.8\times359 = 1364.2\) and \(1364.2\div278\approx4.9\space L\).

Answer:

The new volume of the methane gas is approximately \(4.9\space L\).