STP Formula : Definition, Solved Examples

STP Formula: Standard temperature is characterized by the freezing point of pure water at sea level, which is equivalent to 0˚C (zero degrees Celsius), 32˚F (32 degrees Fahrenheit), or 273˚K (273.15 degrees Kelvin). Standard pressure is defined as the pressure required to support a 760 mm tall column of mercury at sea level and 0 degrees Celsius. Specifically, standard temperature and pressure (STP) are defined as 0˚C and 1 atmosphere (1 atm) of pressure. The volume of a gas is affected by several variables, including the temperature of the gas, its pressure, and the amount of gas (expressed in moles).

Also Check – Molecular Speed Formula

STP Formula

According to the ideal gas law state volume taken up by a gas relies on the quantity of the gas, temperature, and pressure. Standard temperature and pressure are defined as 0 degrees Celsius and 1 atmosphere of pressure. These gas parameters are essential for calculations in the fields of chemistry and physics and are typically evaluated at STP.

Applying the ideal gas law, we can express it as:

P × V = n × R × T

In contrast, when dealing with the parameters:

P stands for Pressure

V represents Volume

n denotes the number of moles

R is the molar gas constant

T signifies Temperature

At Standard Temperature and Pressure (STP):

T is equal to T _stp , which equals 273.15 K

P equals P _stp , equating to 1 atm

n is equivalent to 1 mole of gas

R is defined as 0.08206 L-atm/mol-K

V becomes V _stp , calculated as (n × R × T _stp ) / P _stp

This simplifies to ((1 mole) × (0.08206 L-atm/mol-K)) / (1 atm)

Which results in 22.414 L per mole.

Also Check – Mole Fraction Formula

STP Formula Solved Example

Example 1: How can we determine the volume of oxygen, represented by 2.50 moles, when it exerts a pressure of 1500 mm of mercury at a temperature of 20 degrees Celsius?

Solution:

To solve this problem, we'll begin with the knowledge that 1 atmosphere (atm) can support a column of mercury that is 760 mm high. To convert the given pressure into atmospheres, we use the following conversion:

P = (1500 mm Hg) / (760 mm atm⁻¹)

This yields a pressure of approximately 1.97 atmospheres (atm).

Now, we can employ the Ideal Gas Equation to find the volume:

V = (n × R × T) / P

Where:

V represents the volume we want to calculate.

n is the number of moles, given as 2.50 moles of oxygen.

R is the molar gas constant, approximately 0.0821 L·atm/(K·mol).

T stands for temperature, which we convert to Kelvin (K) by adding 273 to 20 degrees Celsius, resulting in 293 K.

P is the pressure we determined as 1.97 atm.

Now, we can calculate:

V = ((2.50 mol) × (0.0821 L·atm/(K·mol)) × (293 K)) / (1.97 atm)

After performing the calculations, we find that the volume of oxygen under these conditions is approximately 30.5 liters (L).

Also Check – Vapor Pressure Formula

Example 2: What is the pressure exerted by 0.75 moles of nitrogen gas in a 10.0-liter container at a temperature of 300 K?

Solution:

Using the Ideal Gas Equation:

P = (n × R × T) / V

Where:

n = 0.75 moles of nitrogen gas.

R ≈ 0.0821 L·atm/(K·mol) (molar gas constant).

T = 300 K (temperature).

V = 10.0 liters (volume).

P = ((0.75 mol) × (0.0821 L·atm/(K·mol)) × (300 K)) / (10.0 L)

P ≈ 1.24 atm

So, the pressure exerted by the nitrogen gas is approximately 1.24 atmospheres.

Also Check – Theoretical Yield Formula

Example 3: How many moles of carbon dioxide are there in a 5.0-liter container at 25 degrees Celsius and a pressure of 3.0 atmospheres?

Solution:

Rearranging the Ideal Gas Equation to solve for n:

n = (P × V) / (R × T)

Where:

P = 3.0 atm (pressure).

V = 5.0 liters (volume).

R ≈ 0.0821 L·atm/(K·mol) (molar gas constant).

T = 25°C + 273 = 298 K (temperature).

n = (3.0 atm × 5.0 L) / (0.0821 L·atm/(K·mol) × 298 K)

n ≈ 0.61 moles

So, there are approximately 0.61 moles of carbon dioxide in the container.

Example 4 : If 4.0 moles of hydrogen gas are in a 20.0-liter container at standard temperature and pressure (STP), what is the pressure?

Solution:

At STP, the temperature is 273.15 K, and the pressure is 1 atm. We can use the Ideal Gas Equation to find the pressure:

P = (n × R × T) / V

Where:

n = 4.0 moles of hydrogen gas.

R ≈ 0.0821 L·atm/(K·mol) (molar gas constant).

T = 273.15 K (STP temperature).

V = 20.0 liters (volume).

P = ((4.0 mol) × (0.0821 L·atm/(K·mol)) × (273.15 K)) / (20.0 L)

P ≈ 1.82 atm

So, the pressure of the hydrogen gas at STP is approximately 1.82 atmospheres.