CHEMISTRY (please help)

Question

" Solve the problem; show your work in the space provided and circle the answer. Express the answer using proper significant figures and units."

1. A sample of hydrogen gas has a volume of 4.4 L at a pressure of 800. torr. If the pressure decreases to 400. torr, what will the new volume be?
2. A sample of nitrogen occupies 1.00 L at a temperature of 250. K. What volume would it occupy at 1500. K.?
3. A typical weather balloon contains approximately 563 L of hydrogen gas when it is released. If the temperature and pressure at the surface are 288 K and 1.00 atm when the balloon is released, what will its volume be at 32.0 km above the surface, where temperature and pressure are 299 K and 8.57x10-3 atm?
4. Sodium metal and chlorine gas can be produced industrially by passing an electric current thorugh molten sodium chloride:

2 NaCl(1) → 2 Na(1) + Cl2(g)

What volume of Cl2 at 293 K (20.°C) and 1.00 atm can be obtained from 68.0 g NaCl using the reaction? (MNaCl = 58.44 g/mol; R = 0.0821 L•atm/[K•mol])

please show work! thank you

Answer 1

These gas problems deal with temperature (T), pressure (P) and volume (V) and sometimes moles (n). There are different gas laws that you must learn in order to answer these problems

A sample of nitrogen occupies 1.00 L at a temperature of 250. K. What volume would it occupy at 1500. K.?

Given:

Initial volume (V1) = 1.00 L

Initial Temperature (T1) = 250K

Temperature (T2) = 1500K

Asked to find:

Final volume (V2)

Use Charles Law (constant pressure): V1/T1 = V2/T2 and solve for V2

V2 = V1T2 / T1 = (1.00 L)(1500K) / 250 K

V2 = final volume = 6.00 L (3 sig figs)

A typical weather balloon contains approximately 563 L of hydrogen gas when it is released. If the temperature and pressure at the surface are 288 K and 1.00 atm when the balloon is released, what will its volume be at 32.0 km above the surface, where temperature and pressure are 299 K and 8.57x10-3 atm?

In this problem we are given the following info:

V1 = 563 L

T1 = 288K

P1 = 1.00 atm

T2 = 299K

P2 = 8.57x10^-3 atm

The 32.0 km above the surface is not relevant to this problem since they give you the final T and P.

We are asked to find the final volume (V2). Here you would use the combined gas law:

P1V1/T1 = P2V2/T2

(1.00 atm)(563 L) / 288K = (8.57x10^-3 atm)(V2) / 299K

Solving for V2 we have...

(1.00)(563)(299) / 8.57x10^-3)(288) = V2

V2 = 68,200 L (3 sig figs)

Sodium metal and chlorine gas can be produced industrially by passing an electric current thorugh molten sodium chloride:

2 NaCl(1) → 2 Na(1) + Cl2(g)

What volume of Cl2 at 293 K (20.°C) and 1.00 atm can be obtained from 68.0 g NaCl using the reaction? (MNaCl = 58.44 g/mol; R = 0.0821 L•atm/[K•mol])

For this problem we will need to find the mols of NaCl used and convert that to mols of Cl₂ produced. Then convert the moles of Cl₂ gas produced to a volume of Cl₂ gas using the ideal gas law PV = nRT (see below)

mols NaCl used = 68.0 g NaCl x 1 mol NaCl / 58.44 g = 1.164 mols NaCl

mols Cl₂ gas produced = 1.164 mols NaCl x 1 mol Cl₂ / 2 mol NaCl = 0.5820 mols Cl₂

Using the ideal gas law, we now convert this to volume (liters) of Cl₂:

PV = nRT

P = pressure in atm = 1.00 atm

V = volume in liters = ?

n= mols = 0.5820 mols

R = gas constant = 0.0821 Latm/Kmol

T = temp in K = 293K

Solving for V, we have V = nRT/P = (0.5820)(0.0821)(293) / 1.00

V = 14.0 liters

Answer 2

Here's how to do the first one:

1. A sample of hydrogen gas has a volume of 4.4 L at a pressure of 800. torr. If the pressure decreases to 400. torr, what will the new volume be?

P₁=800. torr

V₁=4.4 L

P₂=400. torr

V₂=? L

P₁V₁=P₂V₂

V₂=P₁V₁/P₂

V₂=(800.×4.4)/400.

V₂=8.8 L

The answer is rounded correctly to two sig figs.

All of these questions use combined gas law:

P₁V₁/n₁T₁=P₂V₂/n₂T₂

For #4:

Convert g NaCl to moles

convert mol NaCl to moles Cl2

use PV=nRT to solve for V