Gas Laws

We use the ideal gas law: Rewriting in terms of molar mass , using : Given:

Substitute into the formula: Divide: Hence, the molar mass is , matching option (1).

From the ideal gas law, we know that the pressure is directly proportional to the number of moles and inversely proportional to the molar mass: Let the molar mass of gas be and that of gas be . The pressure exerted by gas is 2 atm, and the total pressure after introducing gas is 3 atm. From the ideal gas law: After solving for the relationship between the molar masses, we get: Thus, the correct answer is Option 4: .

- Statement I (Charles' law): Correct. According to Charles' law, the volume of a gas is directly proportional to its temperature at constant pressure.
- Statement II (Graham's law): Correct. The rate of diffusion of a gas is inversely proportional to its density, at constant pressure and temperature.
- Statement III: Correct. The kinetic energy of a gas is directly proportional to the absolute temperature (T).
Thus, the correct answer is Option 2: I, II, III.

Charles' law: (at constant pressure). This means as , . Theoretically, if volume becomes zero, the corresponding temperature is absolute zero: This is the point at which all molecular motion theoretically stops. So, if volume is zero, the temperature must be C.

Step 1: Recall the ideal gas law.
For an ideal gas, .
Step 2: Analyze the data.
From to , , indicating ideal behavior. For and , deviates from 1, indicating non-ideal behavior.
Step 3: Conclusion.
The gas behaves ideally in the pressure range 1 to 3 bar. Final Answer:

The ideal gas law is given by: $ is the pressure, is the volume, is the number of moles, is the ideal gas constant, and is the temperature.
We want to find the relationship between the density of the gas and its pressure at a constant temperature .
Density is defined as mass per unit volume: \) can be expressed in terms of the mass of the gas and its molar mass : \) into the ideal gas law: \) , which is the density : \) , and for a specific ideal gas (which has a constant molar mass ), the terms are constant.
Let .
Then the equation becomes: \) $ This shows that the density of an ideal gas at a given temperature is directly proportional to its pressure .
Therefore, .

CO₂ is the most significant greenhouse gas due to its high concentration and persistence in the atmosphere. It absorbs infrared radiation and traps heat. While CH₄ and N₂O are stronger per molecule, their overall concentration is far less than that of CO₂.

Step 1: Analyze segment
In this path, the curve is vertical, meaning temperature is constant while volume changes.
Hence, the process is Isothermal. Step 2: Analyze segment
Here, volume increases but temperature remains constant (horizontal line),
which is a characteristic of an Isobaric process. Step 3: Analyze segment
This segment shows a straight line with constant volume, while temperature decreases.
Therefore, the process is Isochoric. Step 4: Conclusion
The sequence of processes is: Isothermal (CA), Isobaric (AB), Isochoric (BC).

First, calculate the mass of Na in the mixture, which is 20% of 4.0 g, i.e., 0.8 g of Na. Then, use the molar masses of NaCl and NaBr to calculate the fraction of Na that is in NaCl. By setting up the equation for the mass of NaCl, you will find that NaCl constitutes 48% of the mixture.

Rules for determining significant figures: 1.
Non-zero digits are always significant.
2.
Zeros between non-zero digits are significant.
3.
Leading zeros (zeros to the left of the first non-zero digit) are not significant.
They only indicate the position of the decimal point.
4.
Trailing zeros in a number with a decimal point are significant.
5.
Trailing zeros in a number without a decimal point are ambiguous (e.
g.
, 500 could have 1, 2, or 3 s.
f.
).
Scientific notation or an explicit decimal point (like 500.
) removes ambiguity.
A) 0.
0025 - The leading zeros (0.
00) are not significant.
- The non-zero digits 2 and 5 are significant.
- Number of significant figures = 2.
B) 500.
0 - The non-zero digit 5 is significant.
- The zeros between 5 and the decimal point are significant because of the trailing zero after the decimal point.
- The trailing zero after the decimal point (500.
0) is significant.
- All digits 5, 0, 0, 0 are significant.
- Number of significant figures = 4.
C) 2.
0034 - The non-zero digits 2, 3, 4 are significant.
- The zeros between 2 and 3 (2.
0034) are significant.
- All digits 2, 0, 0, 3, 4 are significant.
- Number of significant figures = 5.
So, the number of significant figures in A, B, and C are 2, 4, and 5, respectively.
This matches option (4).

Step 1: Understanding Feasibility Feasibility depends on oxidation strength: - Chlorine is the strongest oxidizing agent, capable of replacing bromine and iodine. - Bromine is weaker, but can replace iodine. - Iodine is the weakest and cannot oxidize bromide ions. Step 2: Evaluating the Reactions - (A) : - Feasible (Chlorine displaces bromine). - (B) : - Feasible (Chlorine displaces iodine). - (C) : - Feasible (Bromine displaces iodine). - (D) : - Not feasible (Iodine cannot displace bromine). Conclusion Thus, the correct answer is:

Step 1: Understanding Feasibility Feasibility depends on oxidation strength: - Chlorine is the strongest oxidizing agent, capable of replacing bromine and iodine. - Bromine is weaker, but can replace iodine. - Iodine is the weakest and cannot oxidize bromide ions. Step 2: Evaluating the Reactions - (A) : - Feasible (Chlorine displaces bromine). - (B) : - Feasible (Chlorine displaces iodine). - (C) : - Feasible (Bromine displaces iodine). - (D) : - Not feasible (Iodine cannot displace bromine). Conclusion Thus, the correct answer is:

Rules for determining significant figures: 1.
Non-zero digits are always significant.
2.
Zeros between non-zero digits are significant.
3.
Leading zeros (zeros to the left of the first non-zero digit) are not significant.
They only indicate the position of the decimal point.
4.
Trailing zeros in a number with a decimal point are significant.
5.
Trailing zeros in a number without a decimal point are ambiguous (e.
g.
, 500 could have 1, 2, or 3 s.
f.
).
Scientific notation or an explicit decimal point (like 500.
) removes ambiguity.
A) 0.
0025 - The leading zeros (0.
00) are not significant.
- The non-zero digits 2 and 5 are significant.
- Number of significant figures = 2.
B) 500.
0 - The non-zero digit 5 is significant.
- The zeros between 5 and the decimal point are significant because of the trailing zero after the decimal point.
- The trailing zero after the decimal point (500.
0) is significant.
- All digits 5, 0, 0, 0 are significant.
- Number of significant figures = 4.
C) 2.
0034 - The non-zero digits 2, 3, 4 are significant.
- The zeros between 2 and 3 (2.
0034) are significant.
- All digits 2, 0, 0, 3, 4 are significant.
- Number of significant figures = 5.
So, the number of significant figures in A, B, and C are 2, 4, and 5, respectively.
This matches option (4).