12. The combined gas law states that pressure and Kelvin temperature of a fixed amount of gas are __ proportional to each, and pressure is __ proportional to the volume of the gas. a) inversely, directly c) directly,exponentially b) inversely, exponentially d) directly inversely 13. Avogadro's Law states that: a) Equal volumes of gases under the same conditions of temperature and pressure contain equal number of molecules b) The size or mass of a particle has no effect on molecules since the distances between the particles are so small c) The molar volume of any gas at STP is 22.4 L d) Pressure is directly proportional to the number of atoms or molecules 14. To find the density of a gas the following equation can be used: a) d=(PV)/(RT) C) d=(PM)/(VnRT) b) d=(RM)/(PT) d) d=(PM)/(RT)

Let's address each question one by one:<br /><br />12. The combined gas law is expressed as \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\), where \(P\) is pressure, \(V\) is volume, and \(T\) is temperature in Kelvin. According to this law:<br />- Pressure is directly proportional to temperature when volume is constant.<br />- Pressure is inversely proportional to volume when temperature is constant.<br /><br />Therefore, the correct answer is:<br />d) directly, inversely<br /><br />13. Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This is a fundamental principle of gas behavior.<br />The correct answer is:<br />a) Equal volumes of gases under the same conditions of temperature and pressure contain equal number of molecules<br /><br />14. To find the density of a gas, we use the ideal gas law equation rearranged for density. The formula for density (\(d\)) is derived from \(PV = nRT\) and is given by:<br />\[ d = \frac{PM}{RT} \]<br />where \(P\) is pressure, \(M\) is molar mass, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.<br />The correct answer is:<br />d) \( d=\frac{P M}{R T} \)