9. what volume will 454 mol of hydrogen occup...
9. what volume will 454 mol of hydrogen occupy at 1.05 atm and 25°c?
Answer
# Explanation:
## Step1: Convert temperature to Kelvin
The formula to convert Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273.15\).
Given \(T = 25^{\circ}C\), then \(T=25 + 273.15=298.15\ K\)
## Step2: Use the ideal gas law \(PV = nRT\)
We need to solve for \(V\), so \(V=\frac{nRT}{P}\)
where \(n = 454\ mol\), \(R=0.0821\ L\cdot atm\cdot K^{-1}\cdot mol^{-1}\), \(T = 298.15\ K\), \(P = 1.05\ atm\)
Substitute the values into the formula:
\(V=\frac{454\times0.0821\times298.15}{1.05}\)
First, calculate the numerator: \(454\times0.0821\times298.15=(454\times0.0821)\times298.15 = 37.2734\times298.15\approx11111.1\)
Then, \(V=\frac{11111.1}{1.05}\approx10582\ L\)
# Answer:
\(10582\ L\)