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The volume of the gas at 800mmHg pressure and 30°C is 480ml.What volume does the gas occupy at STP?

Feb 15

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Feb 15

To find the volume of the gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation:

PV = nRT

Where:

P = pressure (in atm)

V = volume (in liters)

n = number of moles

R = ideal gas constant (0.0821 L·atm/mol·K)

T = temperature (in Kelvin)

First, we need to convert the given pressure from mmHg to atm:

1 atm = 760 mmHg

800 mmHg * (1 atm / 760 mmHg) = 1.053 atm

Next, we need to convert the given temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

30°C + 273.15 = 303.15 K

Now, we can rearrange the ideal gas law equation to solve for V:

V = (nRT) / P

Since we are comparing the volume at two different conditions, the number of moles (n) and the gas constant (R) will remain constant. Therefore, we can write the equation as:

V1 / P1 = V2 / P2

Where:

V1 = initial volume (480 mL)

P1 = initial pressure (1.053 atm)

V2 = final volume (unknown)

P2 = final pressure (1 atm at STP)

Now we can solve for V2:

V2 = (V1 * P2) / P1

V2 = (480 mL * 1 atm) / 1.053 atm

V2 ≈ 456 mL

Therefore, the gas occupies approximately 456 mL at STP.

PV = nRT

Where:

P = pressure (in atm)

V = volume (in liters)

n = number of moles

R = ideal gas constant (0.0821 L·atm/mol·K)

T = temperature (in Kelvin)

First, we need to convert the given pressure from mmHg to atm:

1 atm = 760 mmHg

800 mmHg * (1 atm / 760 mmHg) = 1.053 atm

Next, we need to convert the given temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

30°C + 273.15 = 303.15 K

Now, we can rearrange the ideal gas law equation to solve for V:

V = (nRT) / P

Since we are comparing the volume at two different conditions, the number of moles (n) and the gas constant (R) will remain constant. Therefore, we can write the equation as:

V1 / P1 = V2 / P2

Where:

V1 = initial volume (480 mL)

P1 = initial pressure (1.053 atm)

V2 = final volume (unknown)

P2 = final pressure (1 atm at STP)

Now we can solve for V2:

V2 = (V1 * P2) / P1

V2 = (480 mL * 1 atm) / 1.053 atm

V2 ≈ 456 mL

Therefore, the gas occupies approximately 456 mL at STP.