The volume of a sample of nitrogen is 6.00 liters at 35oC and 740 torr. What volume will it occupy at STP?
(p1v 1/t1) = (P2V2/T2)
I assume you know that STP means 273 C for T and 760 torr for P.
Remember to use 273 + 35 = ? for P1
6.59L
I need the solution
To find the volume of nitrogen at STP (Standard Temperature and Pressure), you need to use the gas laws. STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (760 mmHg or 760 torr).
The gas law that relates volume, temperature, and pressure is known as the combined gas law:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
In this case, you are given:
- P₁ = 740 torr (pressure of the nitrogen sample)
- V₁ = 6.00 liters (initial volume of the nitrogen sample)
- T₁ = 35°C = 35 + 273.15 K (initial temperature of the nitrogen sample)
- P₂ = 760 torr (pressure at STP)
- T₂ = 0°C = 0 + 273.15 K (temperature at STP)
Now, substitute the given values into the gas law equation:
(740 torr × 6.00 L) / (35 + 273.15 K) = (760 torr × V₂) / (0 + 273.15 K)
To solve for V₂, isolate it by cross-multiplying:
(740 torr × 6.00 L) × (0 + 273.15 K) = (760 torr × V₂) × (35 + 273.15 K)
Simplifying the equation further:
(4440 torr × K) = (103672 torr × V₂)
Divide both sides by 103672 torr to solve for V₂:
V₂ = (4440 torr × K) / 103672 torr
Now you know V₂, the volume of the nitrogen sample at STP.