I put together a pc and ant to know if its compatible.
Sapphire Radeon HD 7870 1000MHZ 2GB 4.8GHZ GDDR5 DVI HDMI 2XMINIDP PCI-E Video Card
1 x Intel Core i5 3570K Unlocked Quad Core Processor LGA1155 3.4GHZ Ivy Bridge 6MB Retail
1 x Cooler Master Hyper 212 Evo Direct Touch 4 Heatpipe Heatsink AM2 AM3 LGA1366/1155/1156/2011 120mm
1 x Gigabyte Z77X-D3H ATX LGA1155 Z77 DDR3 3PCI-E16 3PCI-E1 HDMI CrossFireX/SLI SATA3 USB3.0 Motherboard
1 x Corsair CML8GX3M2A1600C9 Vengeance Lowprofile 8GB 2X4GB DDR3-1600 CL9-9-9-24 Dual Channel Memory Kit
1 x Antec Three Hundred Two Mid Tower Gaming Case 302 ATX 3X5.25 6X3.5INT No PS Front USB3.0 & Audio
1 x Corsair CX Series CX600 600W ATX 12V 80 Plus Bronze Power Supply 140mm Fan
1 x Microsoft Windows 7 Home Premium Edition 64Bit SP1 DVD OEM *for NCIX PC Only*
1 x Seagate Barracuda 1TB 7200RPM 64MB SATA 6Gbps 3.5IN Internal Hard Drive - OEM
1 x ASUS DRW-24B1ST 24X SATA DVD Writer OEM Black
Okay - overall a very good build. I'm guessing you're at about $1100 at the moment? You have a pretty solid build.
The only thing I'd recommend is buying an SSD to go along with your build. A Samsung or OCZ 128GB SSD should cost around $75-80 at the moment. You will gain a noticeable increase in general performance with this.
Spending a little more money and upgrading to a Radeon HD7950 is also something to look into.