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1) How many moles of gas occupy 58 L at a pressure of 1.55 atmospheres and a temperature of 222 K?

User Skomisa
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2 Answers

6 votes

To find the moles of the gas , we can use the ideal gas law. Which states -


\:\:\:\:\:\:\:\:\:\star\longrightarrow \sf \underline{PV=nRT} \\

Where:-

  • P is the pressure measured in atmospheres
  • V is the volume measured in liters
  • n is the number of moles.
  • R is the ideal gas constant (0.0821 L atm mol⁻¹ K⁻¹).
  • T is the temperature measured in kelvin.

As per question, we are given that-

  • P=1.55 atm
  • V= 58 L
  • T = 222 K
  • R = 0.08206 L atm mol⁻¹ K⁻¹

Now that we have all the required values, so we can put them all in the Ideal gas law formula and solve for moles -


\:\:\:\:\:\:\:\:\:\star\longrightarrow \sf \underline{PV=nRT} \\


\:\:\:\:\:\:\:\:\:\longrightarrow \sf 1.55 * 58 = n * 0.0821 * 222\\


\:\:\:\:\:\:\:\:\:\longrightarrow \sf 89.9 = n * 18.2262\\


\:\:\:\:\:\:\:\:\:\longrightarrow \sf n * 18.2262 =89.9\\


\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf n = (89.9)/(18.2262)\\


\:\:\:\:\:\:\:\:\:\:\:\:\longrightarrow \sf n =4.9324......\\


\:\:\:\:\:\: \:\:\:\:\:\:\longrightarrow \sf \underline{n =4.93 \:moles }\\

Therefore, 4.93 moles of gas will be occupied 58 L at a pressure of 1.55 atmospheres and a temperature of 222K.

User Raja
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7.8k points
7 votes

Answer:

4.93 moles

Step-by-step explanation:

To find how many moles of gas pressure occupy 58 L at a pressure of 1.55 atmospheres and a temperature of 222 K, use the ideal gas law.

Ideal Gas Law


\boxed{\sf PV=nRT}

where:

  • P is the pressure measured in atmospheres (atm).
  • V is the volume measured in liters (L).
  • n is the number of moles.
  • R is the ideal gas constant (0.08206 L atm mol⁻¹ K⁻¹).
  • T is the temperature measured in kelvin (K).

As we are solving for the number of moles, rearrange the equation to isolate n:


\implies \sf n=(PV)/(RT)

Given values:

  • P = 1.55 atm
  • V = 58 L
  • R = 0.08206 L atm mol⁻¹ K⁻¹
  • T = 222 K

Substitute the values into the formula and solve for n:


\implies \sf n=(1.55 \cdot 58)/(0.08206 \cdot 222)


\implies \sf n=(89.9)/(18.21732)


\implies \sf n=4.93\;mol\; (3\;s.f.)

Therefore, 4.93 moles of gas occupy a volume of 58 L at a pressure of 1.55 atm and a temperature of 222 K.

User William Leara
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