1.what percent of sample nitrogen must be allowed to escape if its temperature ,pressure and volume are to be changed for 220C,3atm&1.65L to 110C,.7atm&1L?

2.a quantity of gas is collected in a graduated tube over mercury.the volume of gas at 20C is 50 ml calculate vol. at STP

(i)if level of mercury in tube is 100mm above the outside mercury level

if level of mercury in tube is 100mm below the outside mercury level

in both cases barometer reads 750 torr

To tackle your questions, we need to apply some fundamental gas laws and principles. Let's break down each question step by step.

1. Calculating the Percentage of Nitrogen to Escape

To determine the percentage of nitrogen that must escape when changing the conditions of temperature, pressure, and volume, we can use the Ideal Gas Law, which is expressed as:

PV = nRT

Where:

• P = pressure (in atm)
• V = volume (in liters)
• n = number of moles of gas
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature (in Kelvin)

First, we need to convert the temperatures from Celsius to Kelvin:

• 220°C = 220 + 273.15 = 493.15 K
• 110°C = 110 + 273.15 = 383.15 K

Now, we can calculate the initial and final moles of nitrogen using the Ideal Gas Law.

Initial Conditions

For the initial state (220°C, 3 atm, 1.65 L):

Using the Ideal Gas Law:

n_initial = (P * V) / (R * T)

Substituting the values:

n_initial = (3 atm * 1.65 L) / (0.0821 L·atm/(K·mol) * 493.15 K)

Calculating this gives:

n_initial ≈ 0.100 moles

Final Conditions

For the final state (110°C, 0.7 atm, 1 L):

n_final = (P * V) / (R * T)

Substituting the values:

n_final = (0.7 atm * 1 L) / (0.0821 L·atm/(K·mol) * 383.15 K)

Calculating this gives:

n_final ≈ 0.021 moles

Calculating the Escape Percentage

Now, we can find out how much nitrogen must escape:

n_escaped = n_initial - n_final

n_escaped = 0.100 - 0.021 = 0.079 moles

To find the percentage of nitrogen that must escape:

Percentage Escaped = (n_escaped / n_initial) * 100

Percentage Escaped = (0.079 / 0.100) * 100 ≈ 79%

2. Volume of Gas at STP

For the second question, we need to calculate the volume of gas at Standard Temperature and Pressure (STP), which is defined as 0°C (273.15 K) and 1 atm (760 torr).

Case 1: Mercury Level 100 mm Above Outside Level

In this case, the pressure of the gas is the atmospheric pressure minus the height of the mercury column:

P_gas = P_atm - h

Where:

• P_atm = 750 torr
• h = 100 mm = 100 torr

Thus:

P_gas = 750 torr - 100 torr = 650 torr

Now, we can use the combined gas law to find the volume at STP:

(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂

Where:

• P₁ = 650 torr
• V₁ = 50 ml
• T₁ = 293.15 K (20°C)
• P₂ = 760 torr
• T₂ = 273.15 K

Rearranging the equation to solve for V₂ gives:

V₂ = (P₁ * V₁ * T₂) / (P₂ * T₁)

Substituting the values:

V₂ = (650 torr * 50 ml * 273.15 K) / (760 torr * 293.15 K)

Calculating this gives:

V₂ ≈ 43.5 ml

Case 2: Mercury Level 100 mm Below Outside Level

In this scenario, the pressure of the gas is the atmospheric pressure plus the height of the mercury column:

P_gas = P_atm + h

Thus:

P_gas = 750 torr + 100 torr = 850 torr