When the following molecular equation is balanced using the smallest possible integer coefficients, the values of these coefficients are:

phosphorus (P4) (s) + chlorine (g)----> phosphorus trichloride (l)

This looks like a relatively simple problem. What is the trouble you have understanding it? We can get it straightened out now.

P4 + 6Cl2 ==> 4PCl3

I DIDN'T GET HOW THE PCI_3_ why, didn't the P have P_4_ , that's what i didn't get. and i had that answer but i wanted to make sure it was right

I think the trouble you are having is that you are trying to balance the equation by writing the formula. That is, from your description, you are trying to make the P4 balance when writing the formula of PCl3. Converting the word equation to the chemical equation is one step. Balancing the chemical equation is a second step and has nothing to do with the first step. So we look at the word equation and convert that to the chemical equation. That makes it

P4 + Cl2 ==> PCl3. (The name phosphorus trichloride tells you the formula is PCl3.
Now balancing the chemical equation is a separate step.(Note: The FIRST rule in balancing equations is what you can't do. You may not change the subscripts; you may change ONLY coefficients when balancing an equation.)
We know we must have 4 P atoms on the right so we place a coefficient of 4 for PCl3
P4 + Cl2 ==> 4PCl3.
That tells us we have 12 Cl atoms on the right; to get 12 on the left we need to add a 6 as a coefficient for Cl2.
P4 + 6Cl2 ==> 4PCl3.
(Extra: To give an example of my note above, I often used this in class.
Mg + O2 ==> MgO. Students invariably tried to balance it by making it read
Mg + O2 ==>MgO2. But you see that doesn't work because MgO is the formula for magnesium oxide and there is no such animal as MgO2. You balance by changing coefficients and this one would be balanced by 2Mg + O2 ==> 2MgO.)
I hope this helps. Isn't chemistry fun?

Oh i ubderstand it better now, thanks a lot. ummm chemistry is harddd, so glad that's not my major

To balance the chemical equation, we need to ensure that there are the same number of each type of atom on both sides of the equation.

Let's start by counting the number of atoms for each element in the unbalanced equation:

Phosphorus (P): 4 atoms on the left (P4) and 1 atom on the right (PCl3)
Chlorine (Cl): 1 atom on the left (Cl2) and 3 atoms on the right (PCl3)

Now, let's balance the equation step by step:

1. Balance the phosphorus atoms:
Since there are 4 phosphorus atoms on the left, we need to put a coefficient of 4 in front of phosphorus trichloride (PCl3):

P4 + Cl2 -> 4PCl3

2. Balance the chlorine atoms:
Since there are 2 chlorine atoms on the left (as Cl2), we need to put a coefficient of 2 in front of chlorine (Cl2):

P4 + 2Cl2 -> 4PCl3

Now both sides have 4 phosphorus atoms and 6 chlorine atoms.

Therefore, the balanced equation is:

P4 + 2Cl2 → 4PCl3

The coefficients are 1, 2, and 4 for phosphorus (P4), chlorine (Cl2), and phosphorus trichloride (PCl3), respectively.