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Chapter 11: Problem 90

A sample of Ne gas in a 10.0-L container at \(25.0^{\circ} \mathrm{C}\) exerts a pressure of \(7.35 \mathrm{~atm}\). What is the number of moles of Ne in the container? What is the mass in grams of the Ne?

Short Answer

Expert verified
The number of moles of Ne in the container is approximately 3.019 moles. The mass of Ne in the container is approximately 60.91 grams.

Step by step solution

01

Identify the known values and convert temperature to Kelvin

We are given: - Volume of the container (V) = 10.0 L - Pressure (P) = 7.35 atm - Temperature (T) = 25.0 °C To convert the temperature from Celsius to Kelvin, we use the formula: \(T_{(K)} = T_{(°C)} + 273.15\) Now, calculate the temperature in Kelvin: \(T_{(K)} = 25.0 + 273.15 = 298.15 K\)
02

Use the Ideal Gas Law equation to find the number of moles

The Ideal Gas Law equation is given by: \(PV = nRT\) Where: - P is the pressure in atm - V is the volume in L - n is the number of moles - R is the gas constant, \(R = 0.0821 \frac{\mathrm{L\cdot atm}}{\mathrm{mol \cdot K}}\) - T is the temperature in Kelvin We know the values of P, V, R, and T. We can solve for n: \(n = \frac{PV}{RT}\) Now, plug in the values: \(n = \frac{7.35 \cdot 10.0}{0.0821 \cdot 298.15}\) Calculate the value of n: \(n = 3.019 \mathrm{~mol}\) So, there are about 3.019 moles of Ne in the container.
03

Calculate the mass of Ne using its molar mass

To find the mass (m) of Ne, we can use the formula: \(m = n \cdot M\) Where - n is the number of moles - M is the molar mass of Ne The molar mass of Ne is 20.18 g/mol. Now, plug in the values: \(m = 3.019 \cdot 20.18\) Calculate the mass: \(m = 60.91 \mathrm{~g}\) So, the mass of Ne in the container is approximately 60.91 grams.

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Most popular questions from this chapter

According to the ideal gas model, why does the chemical identity of a gas not matter when it comes to producing pressure?

The Kelvin temperature of a gas is doubled. At the same time, its volume is cut in half by compressing it with a piston. What happens to the pressure of the gas? (Hint: Set \(T_{f}=2 T_{i}\) and \(\left.V_{f}=0.5 V_{i}\right)\)

A sample of argon at \(0.0^{\circ} \mathrm{C}\) and \(700.0 \mathrm{~mm} \mathrm{Hg}\) occupies \(15.0 \mathrm{~mL}\). What is its volume at STP?

How does a gas create pressure?

Consider two identical \(1-\mathrm{L}\) containers, both at room temperature \((300 \mathrm{~K})\). One of them contains 1 mole of helium gas, and the other contains 1 mole of hydrogen gas. Is the pressure higher in the helium container, higher in the hydrogen container, or the same in the two containers?
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