pv nrt solve for r
Understand the Problem
The question is asking to solve the ideal gas law equation for the variable 'r'. In the equation PV = nRT, we need to isolate 'R' (the gas constant). The high-level approach will involve rearranging the equation to express 'R' in terms of the other variables.
Answer
$$ R = \frac{PV}{nT} $$
Answer for screen readers
$$ R = \frac{PV}{nT} $$
Steps to Solve
- Identify the ideal gas law equation
The ideal gas law is given by the equation ( PV = nRT ) where:
- ( P ) is the pressure of the gas
- ( V ) is the volume of the gas
- ( n ) is the number of moles of the gas
- ( R ) is the gas constant
- ( T ) is the absolute temperature of the gas
- Rearranging the equation
To solve for ( R ), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by ( nT ).
Starting with $$ PV = nRT $$
We can rearrange it as follows:
$$ R = \frac{PV}{nT} $$
- Finalize the expression for R
Now we have ( R ) isolated, and it is expressed in terms of the other variables.
The final equation is:
$$ R = \frac{PV}{nT} $$
$$ R = \frac{PV}{nT} $$
More Information
The gas constant ( R ) relates the amount of gas, its temperature, pressure, and volume. The value of ( R ) can vary depending on the units used, such as ( R = 0.0821 , \text{L atm/(K mol)} ) or ( R = 8.314 , \text{J/(K mol)} ).
Tips
- Forgetting to divide both ( P ) and ( V ) by ( n ) and ( T ), which would lead to an incorrect equation.
- Confusing the variables and their meanings, especially ( n ) (moles) and ( R ) (gas constant).
- Not keeping track of units when substituting values.
