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Question: The best laboratory vacuum has a pressure of about,1×10-18atmor,1.01×10-13pascal. How many gas molecules are there per cubic centimeter in such a vacuum at 293 k?

Short Answer

Expert verified

Answer

Total of gas molecules25moleculescm3are there per cubic centimeter in such a vacuum at 293 k .

Step by step solution

01

Determine the concept 

By using ideal gas equation, i.e. pv = nRT we can find the number of mole of gas and then find the total number of gas molecule per cubic centimeter at 293 k .

Formula is as follow:

pv = nRT

Here, p is pressure, v is volume, T is temperature, R is universal gas constant and n is number of moles.

02

Determine the number of gas molecules in a vacuum at 293 k

Initially, find the number of mole of the gas by using ideal gas equation,

pv=nRTn=pvRT

Substitute the given values and solve:

n=1.01×10-13×1×10-68.31×293n=4.1×10-23mol

Use this value to find the total number of gas molecules. The formula is,

N=nNA

Here, NA is Avogadro’s number.

N=4.1×10-23×6.02×1023

N=25moleculescm3

Hence, 25moleculescm3gas molecules are there per cubic centimeter in such a vacuum at 293 k.

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Most popular questions from this chapter

The dot in Figre 19-18bpresents the initial state of a gas, and the isotherm through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the change Δ·¡intin the internal energy of the gas is positive, negative, or zero: (a) the gas moves up along the isotherm, (b) it moves down along the isotherm, (c) it moves to anywhere in region, and (d) it moves to anywhere in region.

A quantity of ideal gas at 10°°äand 100 k±Ê²¹occupies a volume of.2.50 â¶Ä³¾3

  1. How many moles of the gas are present?
  2. If the pressure is now raised to300 k±Ê²¹and the temperature is raised to30°°ä, how much volume does the gas occupy? Assume no leaks.

Compute

  1. The number of moles
  2. The number of molecules in1.00 cm3of an ideal gas at a pressure of100 Paand a temperature of220 K.

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