The question asks about the physical significance of absolute zero according to Charles' Law. We need to recall Charles' Law and the concept of absolute zero to determine its implications for the volume of an ideal gas and molecular motion.
or
\[ \frac{V}{T} = \text{constant} \]where \(V\) is the volume and \(T\) is the absolute temperature (in Kelvin).
A) It is the temperature at which the volume of an ideal gas would theoretically become zero — all molecular motion ceases; it is the lowest theoretically possible temperature. This statement accurately describes the physical significance of absolute zero as derived from Charles' Law and the kinetic theory of gases. At this temperature, an ideal gas would occupy zero volume, and all atomic/molecular motion would stop, representing the lowest possible energy state.
The question asks about Gay-Lussac's Law (also known as Amontons' Law), which describes the relationship between the pressure and temperature of a fixed amount of gas when its volume is kept constant. We need to identify the correct mathematical and conceptual statement of this law.
Correct Option: D) Directly proportional to absolute temperature: P ∝ T at constant V and n, i.e., P/T = constant (P₁/T₁ = P₂/T₂)
This option accurately describes Gay-Lussac's Law. It correctly states that pressure (\(P\)) is directly proportional to absolute temperature (\(T\)) when volume (\(V\)) and the amount of gas (\(n\)) are constant. It also provides the correct mathematical expressions for this relationship.
The question asks about Avogadro's Law. This law describes the relationship between the volume of a gas and the number of moles (or molecules) of the gas, under specific conditions of temperature and pressure.
A) Equal number of molecules — V ∝ n at constant T and P, where n = number of moles (Avogadro's law, 1811). This statement perfectly matches the definition and mathematical representation of Avogadro's Law. If the number of moles (\(n\)) is the same, then the number of molecules (which is \(n \times N_A\)) must also be the same.
The question asks for the Combined Gas Law, which relates the pressure (P), volume (V), and temperature (T) of a fixed amount of gas. This law is derived by combining Boyle's Law, Charles's Law, and Gay-Lussac's Law.
Boyle's Law: For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume.
\[ P \propto \frac{1}{V} \quad \text{or} \quad PV = \text{constant} \]Charles's Law: For a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
\[ V \propto T \quad \text{or} \quad \frac{V}{T} = \text{constant} \]Gay-Lussac's Law: For a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
\[ P \propto T \quad \text{or} \quad \frac{P}{T} = \text{constant} \]Combining these laws: We can see that pressure is proportional to temperature and inversely proportional to volume. Similarly, volume is proportional to temperature and inversely proportional to pressure. This leads to the combined relationship:
\[ PV \propto T \]To turn this proportionality into an equation, we introduce a constant:
\[ \frac{PV}{T} = \text{constant} \]This means that for a fixed amount of gas under two different sets of conditions (initial and final), the ratio \(\frac{PV}{T}\) remains the same:
\[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \]This is the mathematical expression for the Combined Gas Law.
D) PV/T = constant, i.e., P₁V₁/T₁ = P₂V₂/T₂
This option correctly represents the Combined Gas Law, which states that for a fixed amount of gas, the ratio of the product of pressure and volume to the absolute temperature is constant.
A) P/VT = constant
This is incorrect. The correct relationship is \(PV/T = \text{constant}\), not \(P/(VT)\). This would imply that pressure is directly proportional to the product of volume and temperature, which contradicts the individual gas laws (e.g., Boyle's Law).
B) P₁V₁/T₁² = P₂V₂/T₂²
This is incorrect. The temperature term in the Combined Gas Law is to the power of one, not two. Squaring the temperature term is not part of the standard gas laws.
C) P₁V₁T₁ = P₂V₂T₂
This is incorrect. This implies that the product of pressure, volume, and temperature is constant, which is not true. The temperature should be in the denominator, not the numerator.
The question asks for the correct form of the Ideal Gas Equation. We need to recall the standard formulation of the ideal gas law and identify the option that matches it, along with correctly defining the terms involved.
Correct Option: B) PV = nRT, where P = pressure, V = volume, n = moles of gas, R = universal gas constant, T = absolute temperature
This option perfectly matches the standard form of the Ideal Gas Equation and correctly defines all the variables.
The question asks for the value of the Universal Gas Constant (R) in SI units. We need to identify which of the given options represents R in SI units and its correct numerical value.
C) \(R = 8.314 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} (= 8.314 \text{ Pa} \cdot \text{m}^3 \cdot \text{mol}^{-1} \cdot \text{K}^{-1})\). This option correctly provides the value of the Universal Gas Constant