Question

if an ideal gas has a pressure of 6.59 atm, a temperature of 38.90°c, and a volume of 47.35 l, how many moles of gas are in the sample?

n = mol

Explanation:

Step1: Convert temperature to Kelvin

The formula to convert Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273.15\).
Given \(T = 38.90^{\circ}C\), then \(T=(38.90 + 273.15)K=312.05K\)

Step2: Use the ideal - gas law \(PV=nRT\)

The ideal - gas law is \(PV=nRT\), where \(P\) is pressure (\(P = 6.59atm\)), \(V\) is volume (\(V = 47.35L\)), \(n\) is the number of moles (what we want to find), \(R\) is the ideal - gas constant (\(R=0.0821\frac{L\cdot atm}{mol\cdot K}\)), and \(T\) is temperature in Kelvin.
We can solve for \(n\) by rearranging the formula: \(n=\frac{PV}{RT}\)
Substitute the values: \(n=\frac{6.59atm\times47.35L}{0.0821\frac{L\cdot atm}{mol\cdot K}\times312.05K}\)
First, calculate the numerator: \(6.59\times47.35 = 312.0365\)
Then, calculate the denominator: \(0.0821\times312.05=25.629305\)
Now, \(n=\frac{312.0365}{25.629305}\approx12.17\)

Answer:

\(12.2\) (rounded to three significant figures)