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How many atoms are in a 2.0 cm×2.0 cm×2.0 cm cube of aluminum?
20. Heat and Temperature
Moles and Avogadro's Number
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A rigid container has a volume of . It contains a ideal gas at . How many moles are in the container?
A
2.1
B
5.6
C
10
D
12
E
15
F
4.3
Verified step by step guidance1
Start by identifying the known values: the volume \( V = 0.14 \, \text{m}^3 \), the temperature \( T = 200^\circ \text{C} \), and the pressure \( P = 1.2 \, \text{atm} \).
Convert the temperature from Celsius to Kelvin using the formula \( T(K) = T(^\circ C) + 273.15 \).
Convert the pressure from atmospheres to pascals using the conversion factor \( 1 \, \text{atm} = 101325 \, \text{Pa} \).
Use the ideal gas law \( PV = nRT \) to solve for the number of moles \( n \). Here, \( R \) is the ideal gas constant \( 8.314 \, \text{J/mol} \cdot \text{K} \).
Rearrange the ideal gas law to solve for \( n \): \( n = \frac{PV}{RT} \). Substitute the known values into this equation to find the number of moles.
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