Question

question 10 (0.0862 points)
which of the following statements is true for gases?
the temperature of a gas is inversely proportional to its pressure.
the volume of a gas is directly proportional to the pressure in torr.
the pressure of a gas is due to collisions of the gas molecules.
all of these are true

question 11 (0.0862 points)
what is the molecular formula of a compound given the molar mass of the compound is 62.2 g/mol and the empirical formula is c₂h₇?
c₆h₂₁
c₄h₁₄
c₂h₇
none of these

Explanation:

Question 10

• Analyze the first option: By the ideal gas law \(PV = nRT\), temperature (\(T\)) is directly proportional to pressure (\(P\)) when volume (\(V\)) and amount (\(n\)) are constant, so the first statement is false.
• Analyze the second option: From \(PV = nRT\), volume (\(V\)) is inversely proportional to pressure (\(P\)) (at constant \(T\) and \(n\)), so the second statement is false.
• Analyze the third option: Gas pressure is caused by gas molecules colliding with the container walls, so this statement is true.
• The fourth option is false as the first two are false.

Step 1: Calculate the molar mass of the empirical formula \(C_2H_7\)

The molar mass of \(C\) is \(12.01\space g/mol\) and \(H\) is \(1.008\space g/mol\). For \(C_2H_7\), molar mass \(M_{empirical}=2\times12.01 + 7\times1.008\)
\(M_{empirical}=24.02+7.056 = 31.076\space g/mol\)

Step 2: Find the ratio of the molar mass of the compound to the empirical formula

Let \(n\) be the ratio. \(n=\frac{M_{molecular}}{M_{empirical}}=\frac{62.2}{31.076}\approx2\)

Step 3: Determine the molecular formula

Multiply the empirical formula by \(n = 2\). So the molecular formula is \(C_{2\times2}H_{7\times2}=C_4H_{14}\)

Answer:

The pressure of a gas is due to collisions of the gas molecules. (The option with this statement)

Question 11